Question 1
Solve. Remember there are two solutions
a) $x^2=9$
a
$x=3$ or $x=-3$
Question ID: 20280010010
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b) $x^2=16$
a
$x=4$ or $x=-4$
Question ID: 20280010020
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c) $x^2=49$
a
$x=7$ or $x=-7$
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d) $x^2=81$
a
$x=9$ or $x=-9$
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e) $x^2=121$
a
$x=11$ or $x=-11$
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f) $x^2=400$
a
$x=20$ or $x=-20$
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Question 2
Solve
a) $(x-5)^2=0$
a
$x=5$
Question ID: 20280020010
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b) $(x-8)^2=0$
a
$x=8$
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c) $(x+3)^2=0$
a
$x=-3$
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d) $(x+7)^2=0$
a
$x=-7$
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e) $(x-12)^2=0$
a
$x=12$
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f) $(x+67)^2=0$
a
$x=-67$
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Question 3
Solve
a) $x^2+6x+9=0$
a
$x=-3$
Question ID: 20280030010
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b) $x^2+10x+25=0$
a
$x=-5$
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c) $x^2+16x+64=0$
a
$x=-8$
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d) $x^2-6x+9=0$
a
$x=3$
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e) $x^2-2x+1=0$
a
$x=1$
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f) $x^2-20x+100=0$
a
$x=10$
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Question 4
Solve. Remember there are two solutions
a) $(x-2)^2=25$
a
$x=7$ or $x=-3$
Question ID: 20280040010
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b) $(x-5)^2=36$
a
$x=11$ or $x=-1$
Question ID: 20280040020
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c) $(x-9)^2=81$
a
$x=18$ or $x=0$
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d) $(x+1)^2=100$
a
$x=9$ or $x=-11$
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e) $(x+7)^2=49$
a
$x=0$ or $x=-14$
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f) $(x+14)^2=144$
a
$x=-2$ or $x=-26$
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Question 5
Solve by forming a perfect square on the left hand side
a) $x^2+8x+16=25$
a
$x=1$ or $x=-9$
Question ID: 20280050010
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b) $x^2+12x+36=64$
a
$x=2$ or $x=-14$
Question ID: 20280050020
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c) $x^2+22x+121=9$
a
$x=-8$ or $x=-14$
Question ID: 20280050030
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d) $x^2-4x+4=1$
a
$x=1$ or $x=3$
Question ID: 20280050040
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e) $x^2-14x+49=100$
a
$x=17$ or $x=-3$
Question ID: 20280050050
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f) $x^2-24x+144=49$
a
$x=5$ or $x=19$
Question ID: 20280050060
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Question 6
Solve by completing the square
a) $x^2+10x+21=0$
a
$x=-3$ or $x=-7$
Question ID: 20280060010
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b) $x^2+6x+8=0$
a
$x=-2$ or $x=-4$
Question ID: 20280060020
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c) $x^2+16x+39=0$
a
$x=-3$ or $x=-13$
Question ID: 20280060030
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d) $x^2-18x-19=0$
a
$x=19$ or $x=-1$
Question ID: 20280060040
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e) $x^2-2x-63=0$
a
$x=-7$ or $x=9$
Question ID: 20280060050
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f) $x^2-22x-23=0$
a
$x=-1$ or $x=23$
Question ID: 20280060060
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Question 7
Solve. Remember there are two solutions
a) $x^2=\frac19$
a
$x=\frac13$ or $x=-\frac13$
Question ID: 20280070010
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b) $x^2=\frac{1}{25}$
a
$x=\frac15$ or $x=-\frac15$
Question ID: 20280070020
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c) $x^2=\frac{1}{4}$
a
$x=\frac12$ or $x=-\frac12$
Question ID: 20280070030
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d) $x^2=\frac{9}{16}$
a
$x=\frac34$ or $x=-\frac34$
Question ID: 20280070040
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e) $x^2=\frac{25}{64}$
a
$x=\frac58$ or $x=-\frac58$
Question ID: 20280070050
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f) $x^2=\frac{121}{49}$
a
$x=\frac{11}{7}$ or $x=-\frac{11}{7}$
Question ID: 20280070060
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Question 8
Solve
a) $(x+1)^2=\frac19$
a
$x=-\frac23$ or $x=-\frac43$
Question ID: 20280080010
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b) $(x-4)^2=\frac{4}{25}$
a
$x=\frac{18}{5}$ or $x=\frac{22}{5}$
Question ID: 20280080020
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c) $\left(x+\frac12\right)^2=\frac{9}{16}$
a
$x=\frac14$ or $x=-\frac54$
Question ID: 20280080030
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d) $(x+2)^2-\frac{1}{36}=0$
a
$x=-\frac{11}{6}$ or $x=-\frac{13}{6}$
Question ID: 20280080040
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e) $(x-1)^2-\frac{4}{49}=0$
a
$x=\frac57$ or $x=\frac97$
Question ID: 20280080050
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f) $\left(x+\frac23\right)^2-\frac{1}{81}=0$
a
$x=-\frac79$ or $x=-\frac59$
Question ID: 20280080060
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Question 9
Solve by completing the square
a) $x^2+3x-4=0$
a
$x=1$ or $x=-4$
Question ID: 20280090010
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$\begin{align}x^2+3x-4&=0\\\left[x^2+3x+\frac94\right]-\frac94-4&=0\\\left(x+\frac32\right)^2-\frac{25}{4}&=0\\\left(x+\frac32\right)^2&=\frac{25}{4}\\x+\frac32&=\frac52\quad\text{or}\quad x+\frac32=-\frac52\\x&=1\quad\text{or}\quad x=-4\end{align}$
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b) $x^2+x-2=0$
a
$x=1$ or $x=-2$
Question ID: 20280090020
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$\begin{align}x^2+x-2&=0\\\left[x^2+x+\frac14\right]-\frac14-2&=0\\\left[x^2+x+\frac14\right]-\frac94&=0\\\left(x+\frac12\right)^2-\frac94&=0\\\left(x+\frac12\right)^2&=\frac94\\x+\frac12&=\frac32\quad\text{or}\quad x+\frac12=-\frac32\\x&=1\quad\text{or}\quad x=-2\end{align}$
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c) $x^2-5x-6=0$
a
$x=-1$ or $x=6$
Question ID: 20280090030
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d) $x^2-7x+6=0$
a
$x=1$ or $x=6$
Question ID: 20280090040
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e) $x^2-x-20=0$
a
$x=5$ or $x=-4$
Question ID: 20280090050
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f) $x^2-x-\frac{63}{4}=0$
a
$x=\frac92$ or $x=-\frac72$
Question ID: 20280090060
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Question 10
Solve by completing the square
a) $x^2+3x+\frac{35}{16}=0$
a
$x=-\frac74$ or $x=-\frac54$
Question ID: 20280100010
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b) $x^2-x+\frac{5}{36}=0$
a
$x=\frac16$ or $x=\frac56$
Question ID: 20280100020
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c) $x^2-7x+\frac{187}{16}=0$
a
$x=\frac{11}{4}$ or $x=\frac{17}{4}$
Question ID: 20280100030
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d) $x^2+9x+\frac{713}{36}=0$
a
$x=-\frac{31}{6}$ or $x=-\frac{23}{6}$
Question ID: 20280100040
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e) $x^2-11x+\frac{2989}{100}=0$
a
$x=\frac{49}{10}$ or $x=\frac{61}{10}$
Question ID: 20280100050
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f) $x^2-13x+\frac{3969}{100}=0$
a
$x=\frac{49}{10}$ or $x=\frac{81}{10}$
Question ID: 20280100060
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Question 11
Solve by completing the square
a) $x^2+\frac32x+\frac12=0$
a
$x=-1$ or $x=-\frac12$
Question ID: 20280110010
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b) $x^2+\frac92x+2=0$
a
$x=-4$ or $x=-\frac12$
Question ID: 20280110020
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c) $x^2+\frac13x-\frac23=0$
a
$x=-1$ or $x=\frac23$
Question ID: 20280110030
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d) $x^2-\frac53x-\frac{14}{9}=0$
a
$x=-\frac23$ or $x=\frac73$
Question ID: 20280110040
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e) $x^2-\frac65x-\frac{27}{25}=0$
a
$x=\frac95$ or $x=-\frac35$
Question ID: 20280110050
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f) $x^2-\frac75x-\frac{3}{20}=0$
a
$x=\frac32$ or $x=-\frac{1}{10}$
Question ID: 20280110060
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Question 12
Solve. Remember there are two solutions
a) $x^2=2$
a
$x=\pm\sqrt2$
Question ID: 20280120010
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b) $x^2=6$
a
$x=\pm\sqrt6$
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c) $x^2=11$
a
$x=\pm\sqrt{11}$
Question ID: 20280120030
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d) $x^2=8$
a
$x=\pm\sqrt8$ or $x=\pm2\sqrt2$
Question ID: 20280120040
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e) $x^2=18$
a
$x=\pm\sqrt{12}$ or $x=\pm2\sqrt3$
Question ID: 20280120050
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f) $x^2=45$
a
$x=\pm\sqrt{45}$ or $x=\pm3\sqrt5$
Question ID: 20280120060
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Question 13
Solve
a) $(x-2)^2=2$
a
$x=2\pm\sqrt2$
Question ID: 20280130010
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b) $(x-7)^2=5$
a
$x=7\pm\sqrt5$
Question ID: 20280130020
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c) $(x+3)^2-15=0$
a
$x=-3\pm\sqrt{15}$
Question ID: 20280130030
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d) $\left(x+\sqrt2\right)^2=2$
a
$x=0$ or $x=-2\sqrt2$
Question ID: 20280130040
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e) $\left(x-\sqrt3\right)^2=27$
a
$x=4\sqrt3$ or $x=-2\sqrt3$
Question ID: 20280130050
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f) $\left(x+2\sqrt7\right)^2-112$
a
$x=2\sqrt7$ or $x=-6\sqrt7$
Question ID: 20280130060
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Question 14
Solve by completing the square
a) $x^2+6x+7=0$
a
$x=-3\pm\sqrt2$
Question ID: 20280140010
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b) $x^2-4x+1=0$
a
$x=2\pm\sqrt3$
Question ID: 20280140020
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c) $x^2+14x+39=0$
a
$x=-7\pm\sqrt{10}$
Question ID: 20280140030
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d) $x^2-2x-5=0$
a
$x=1\pm\sqrt6$
Question ID: 20280140040
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e) $x^2-10x+17=0$
a
$x=5\pm2\sqrt2$
Question ID: 20280140050
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f) $x^2+16x-11=0$
a
$x=-8\pm5\sqrt3$
Question ID: 20280140060
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Question 15
Solve by completing the square
a) $x^2+5x+\frac{11}{2}=0$
a
$x=\frac{-5\pm\sqrt3}{2}$
Question ID: 20280150010
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b) $x^2+x-1=0$
a
$x=\frac{-1\pm\sqrt5}{2}$
Question ID: 20280150020
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c) $x^2-7x+\frac{19}{2}=0$
a
$x=\frac{7\pm\sqrt{11}}{2}$
Question ID: 20280150030
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d) $x^2-x+\frac{1}{36}=0$
a
$x=\frac12\pm\frac{\sqrt2}{3}$
or
$x=\frac{3\pm2\sqrt{2}}{6}$
Question ID: 20280150040
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e) $x^2-\frac52x+\frac54=0$
a
$x=\frac{5\pm\sqrt{5}}{4}$
Question ID: 20280150050
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f) $x^2+\frac56x-\frac{1103}{225}=0$
a
$x=\frac53\pm\frac{8\sqrt3}{5}$
or
$x=\frac{25\pm24\sqrt{3}}{15}$
Question ID: 20280150060
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Question 16
Solve by completing the square
a) $x^2+2\sqrt2x-6=0$
a
$x=\sqrt2$ or $x=-3\sqrt2$
Question ID: 20280160010
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b) $x^2-2\sqrt3x-105=0$
a
$x=7\sqrt3$ or $x=-5\sqrt3$
Question ID: 20280160020
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c) $x^2-4\sqrt5x+15=0$
a
$x=\sqrt5$ or $x=3\sqrt5$
Question ID: 20280160030
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d) $x^2-\sqrt{72}x-14=0$
a
$x=-\sqrt2$ or $x=7\sqrt2$
Question ID: 20280160040
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e) $x^2-\sqrt{2}x-\frac14=0$
a
$x=\frac{\sqrt2\pm\sqrt3}{2}$
Question ID: 20280160050
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f) $x^2+\sqrt5x+\frac{117}{100}=0$
a
$x=-\frac{\sqrt5}{2}\pm\frac{\sqrt2}{5}$
or
$x=\frac{-5\sqrt5\pm2\sqrt2}{10}$
Question ID: 20280160060
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Question 17
Solve by completing the square
a) $x^2=16-6x$
a
$x=2$ or $x=-8$
Question ID: 20280170010
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b) $y^2-39=10y$
a
$y=13$ or $y=-3$
Question ID: 20280170020
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c) $x(2x+1)=x^2+78\frac34-2x$
a
$x=\frac{15}{2}$ or $x=-\frac{21}{2}$
Question ID: 20280170030
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d) $x+5+\frac{9}{4x}=0$
a
$x=-\frac12$ or $x=-\frac92$
Question ID: 20280170040
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e) $x^2\left(\frac12+\frac{\sqrt5}{x}\right)=20$
a
$x=2\sqrt5$ or $x=-4\sqrt5$
Question ID: 20280170050
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f) $1=\frac{17-8z\sqrt3}{16z^2}$
a
$z=\frac{-\sqrt3\pm2\sqrt5}{4}$
Question ID: 20280170060
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Question 1
Solve. Remember there are two solutions
a) $x^2=9$
b) $x^2=16$
c) $x^2=49$
d) $x^2=81$
e) $x^2=121$
f) $x^2=400$
Question 2
Solve
a) $(x-5)^2=0$
b) $(x-8)^2=0$
c) $(x+3)^2=0$
d) $(x+7)^2=0$
e) $(x-12)^2=0$
f) $(x+67)^2=0$
Question 3
Solve
a) $x^2+6x+9=0$
b) $x^2+10x+25=0$
c) $x^2+16x+64=0$
d) $x^2-6x+9=0$
e) $x^2-2x+1=0$
f) $x^2-20x+100=0$
Question 4
Solve. Remember there are two solutions
a) $(x-2)^2=25$
b) $(x-5)^2=36$
c) $(x-9)^2=81$
d) $(x+1)^2=100$
e) $(x+7)^2=49$
f) $(x+14)^2=144$
Question 5
Solve by forming a perfect square on the left hand side
a) $x^2+8x+16=25$
b) $x^2+12x+36=64$
c) $x^2+22x+121=9$
d) $x^2-4x+4=1$
e) $x^2-14x+49=100$
f) $x^2-24x+144=49$
Question 6
Solve by completing the square
a) $x^2+10x+21=0$
b) $x^2+6x+8=0$
c) $x^2+16x+39=0$
d) $x^2-18x-19=0$
e) $x^2-2x-63=0$
f) $x^2-22x-23=0$
Question 7
Solve. Remember there are two solutions
a) $x^2=\frac19$
b) $x^2=\frac{1}{25}$
c) $x^2=\frac{1}{4}$
d) $x^2=\frac{9}{16}$
e) $x^2=\frac{25}{64}$
f) $x^2=\frac{121}{49}$
Question 8
Solve
a) $(x+1)^2=\frac19$
b) $(x-4)^2=\frac{4}{25}$
c) $\left(x+\frac12\right)^2=\frac{9}{16}$
d) $(x+2)^2-\frac{1}{36}=0$
e) $(x-1)^2-\frac{4}{49}=0$
f) $\left(x+\frac23\right)^2-\frac{1}{81}=0$
Question 9
Solve by completing the square
a) $x^2+3x-4=0$
b) $x^2+x-2=0$
c) $x^2-5x-6=0$
d) $x^2-7x+6=0$
e) $x^2-x-20=0$
f) $x^2-x-\frac{63}{4}=0$
Question 10
Solve by completing the square
a) $x^2+3x+\frac{35}{16}=0$
b) $x^2-x+\frac{5}{36}=0$
c) $x^2-7x+\frac{187}{16}=0$
d) $x^2+9x+\frac{713}{36}=0$
e) $x^2-11x+\frac{2989}{100}=0$
f) $x^2-13x+\frac{3969}{100}=0$
Question 11
Solve by completing the square
a) $x^2+\frac32x+\frac12=0$
b) $x^2+\frac92x+2=0$
c) $x^2+\frac13x-\frac23=0$
d) $x^2-\frac53x-\frac{14}{9}=0$
e) $x^2-\frac65x-\frac{27}{25}=0$
f) $x^2-\frac75x-\frac{3}{20}=0$
Question 12
Solve. Remember there are two solutions
a) $x^2=2$
b) $x^2=6$
c) $x^2=11$
d) $x^2=8$
e) $x^2=18$
f) $x^2=45$
Question 13
Solve
a) $(x-2)^2=2$
b) $(x-7)^2=5$
c) $(x+3)^2-15=0$
d) $\left(x+\sqrt2\right)^2=2$
e) $\left(x-\sqrt3\right)^2=27$
f) $\left(x+2\sqrt7\right)^2-112$
Question 14
Solve by completing the square
a) $x^2+6x+7=0$
b) $x^2-4x+1=0$
c) $x^2+14x+39=0$
d) $x^2-2x-5=0$
e) $x^2-10x+17=0$
f) $x^2+16x-11=0$
Question 15
Solve by completing the square
a) $x^2+5x+\frac{11}{2}=0$
b) $x^2+x-1=0$
c) $x^2-7x+\frac{19}{2}=0$
d) $x^2-x+\frac{1}{36}=0$
e) $x^2-\frac52x+\frac54=0$
f) $x^2+\frac56x-\frac{1103}{225}=0$
Question 16
Solve by completing the square
a) $x^2+2\sqrt2x-6=0$
b) $x^2-2\sqrt3x-105=0$
c) $x^2-4\sqrt5x+15=0$
d) $x^2-\sqrt{72}x-14=0$
e) $x^2-\sqrt{2}x-\frac14=0$
f) $x^2+\sqrt5x+\frac{117}{100}=0$
Question 17
Solve by completing the square
a) $x^2=16-6x$
b) $y^2-39=10y$
c) $x(2x+1)=x^2+78\frac34-2x$
d) $x+5+\frac{9}{4x}=0$
e) $x^2\left(\frac12+\frac{\sqrt5}{x}\right)=20$
f) $1=\frac{17-8z\sqrt3}{16z^2}$
Answers
Question 1
a) $x=3$ or $x=-3$
b) $x=4$ or $x=-4$
c) $x=7$ or $x=-7$
d) $x=9$ or $x=-9$
e) $x=11$ or $x=-11$
f) $x=20$ or $x=-20$
Question 2
a) $x=5$
b) $x=8$
c) $x=-3$
d) $x=-7$
e) $x=12$
f) $x=-67$
Question 3
a) $x=-3$
b) $x=-5$
c) $x=-8$
d) $x=3$
e) $x=1$
f) $x=10$
Question 4
a) $x=7$ or $x=-3$
b) $x=11$ or $x=-1$
c) $x=18$ or $x=0$
d) $x=9$ or $x=-11$
e) $x=0$ or $x=-14$
f) $x=-2$ or $x=-26$
Question 5
a) $x=1$ or $x=-9$
b) $x=2$ or $x=-14$
c) $x=-8$ or $x=-14$
d) $x=1$ or $x=3$
e) $x=17$ or $x=-3$
f) $x=5$ or $x=19$
Question 6
a) $x=-3$ or $x=-7$
b) $x=-2$ or $x=-4$
c) $x=-3$ or $x=-13$
d) $x=19$ or $x=-1$
e) $x=-7$ or $x=9$
f) $x=-1$ or $x=23$
Question 7
a) $x=\frac13$ or $x=-\frac13$
b) $x=\frac15$ or $x=-\frac15$
c) $x=\frac12$ or $x=-\frac12$
d) $x=\frac34$ or $x=-\frac34$
e) $x=\frac58$ or $x=-\frac58$
f) $x=\frac{11}{7}$ or $x=-\frac{11}{7}$
Question 8
a) $x=-\frac23$ or $x=-\frac43$
b) $x=\frac{18}{5}$ or $x=\frac{22}{5}$
c) $x=\frac14$ or $x=-\frac54$
d) $x=-\frac{11}{6}$ or $x=-\frac{13}{6}$
e) $x=\frac57$ or $x=\frac97$
f) $x=-\frac79$ or $x=-\frac59$
Question 9
a) $x=1$ or $x=-4$
b) $x=1$ or $x=-2$
c) $x=-1$ or $x=6$
d) $x=1$ or $x=6$
e) $x=5$ or $x=-4$
f) $x=\frac92$ or $x=-\frac72$
Question 10
a) $x=-\frac74$ or $x=-\frac54$
b) $x=\frac16$ or $x=\frac56$
c) $x=\frac{11}{4}$ or $x=\frac{17}{4}$
d) $x=-\frac{31}{6}$ or $x=-\frac{23}{6}$
e) $x=\frac{49}{10}$ or $x=\frac{61}{10}$
f) $x=\frac{49}{10}$ or $x=\frac{81}{10}$
Question 11
a) $x=-1$ or $x=-\frac12$
b) $x=-4$ or $x=-\frac12$
c) $x=-1$ or $x=\frac23$
d) $x=-\frac23$ or $x=\frac73$
e) $x=\frac95$ or $x=-\frac35$
f) $x=\frac32$ or $x=-\frac{1}{10}$
Question 12
a) $x=\pm\sqrt2$
b) $x=\pm\sqrt6$
c) $x=\pm\sqrt{11}$
d) $x=\pm\sqrt8$ or $x=\pm2\sqrt2$
e) $x=\pm\sqrt{12}$ or $x=\pm2\sqrt3$
f) $x=\pm\sqrt{45}$ or $x=\pm3\sqrt5$
Question 13
a) $x=2\pm\sqrt2$
b) $x=7\pm\sqrt5$
c) $x=-3\pm\sqrt{15}$
d) $x=0$ or $x=-2\sqrt2$
e) $x=4\sqrt3$ or $x=-2\sqrt3$
f) $x=2\sqrt7$ or $x=-6\sqrt7$
Question 14
a) $x=-3\pm\sqrt2$
b) $x=2\pm\sqrt3$
c) $x=-7\pm\sqrt{10}$
d) $x=1\pm\sqrt6$
e) $x=5\pm2\sqrt2$
f) $x=-8\pm5\sqrt3$
Question 15
a) $x=\frac{-5\pm\sqrt3}{2}$
b) $x=\frac{-1\pm\sqrt5}{2}$
c) $x=\frac{7\pm\sqrt{11}}{2}$
d) $x=\frac12\pm\frac{\sqrt2}{3}$
or
$x=\frac{3\pm2\sqrt{2}}{6}$
e) $x=\frac{5\pm\sqrt{5}}{4}$
f) $x=\frac53\pm\frac{8\sqrt3}{5}$
or
$x=\frac{25\pm24\sqrt{3}}{15}$
Question 16
a) $x=\sqrt2$ or $x=-3\sqrt2$
b) $x=7\sqrt3$ or $x=-5\sqrt3$
c) $x=\sqrt5$ or $x=3\sqrt5$
d) $x=-\sqrt2$ or $x=7\sqrt2$
e) $x=\frac{\sqrt2\pm\sqrt3}{2}$
f) $x=-\frac{\sqrt5}{2}\pm\frac{\sqrt2}{5}$
or
$x=\frac{-5\sqrt5\pm2\sqrt2}{10}$
Question 17
a) $x=2$ or $x=-8$
b) $y=13$ or $y=-3$
c) $x=\frac{15}{2}$ or $x=-\frac{21}{2}$
d) $x=-\frac12$ or $x=-\frac92$
e) $x=2\sqrt5$ or $x=-4\sqrt5$
f) $z=\frac{-\sqrt3\pm2\sqrt5}{4}$
Question 1
Solve. Remember there are two solutions
a) $x^2=9$
b) $x^2=16$
c) $x^2=49$
d) $x^2=81$
e) $x^2=121$
f) $x^2=400$
Question 2
Solve
a) $(x-5)^2=0$
b) $(x-8)^2=0$
c) $(x+3)^2=0$
d) $(x+7)^2=0$
e) $(x-12)^2=0$
f) $(x+67)^2=0$
Question 3
Solve
a) $x^2+6x+9=0$
b) $x^2+10x+25=0$
c) $x^2+16x+64=0$
d) $x^2-6x+9=0$
e) $x^2-2x+1=0$
f) $x^2-20x+100=0$
Question 4
Solve. Remember there are two solutions
a) $(x-2)^2=25$
b) $(x-5)^2=36$
c) $(x-9)^2=81$
d) $(x+1)^2=100$
e) $(x+7)^2=49$
f) $(x+14)^2=144$
Question 5
Solve by forming a perfect square on the left hand side
a) $x^2+8x+16=25$
b) $x^2+12x+36=64$
c) $x^2+22x+121=9$
d) $x^2-4x+4=1$
e) $x^2-14x+49=100$
f) $x^2-24x+144=49$
Question 6
Solve by completing the square
a) $x^2+10x+21=0$
b) $x^2+6x+8=0$
c) $x^2+16x+39=0$
d) $x^2-18x-19=0$
e) $x^2-2x-63=0$
f) $x^2-22x-23=0$
Question 7
Solve. Remember there are two solutions
a) $x^2=\frac19$
b) $x^2=\frac{1}{25}$
c) $x^2=\frac{1}{4}$
d) $x^2=\frac{9}{16}$
e) $x^2=\frac{25}{64}$
f) $x^2=\frac{121}{49}$
Question 8
Solve
a) $(x+1)^2=\frac19$
b) $(x-4)^2=\frac{4}{25}$
c) $\left(x+\frac12\right)^2=\frac{9}{16}$
d) $(x+2)^2-\frac{1}{36}=0$
e) $(x-1)^2-\frac{4}{49}=0$
f) $\left(x+\frac23\right)^2-\frac{1}{81}=0$
Question 9
Solve by completing the square
a) $x^2+3x-4=0$
b) $x^2+x-2=0$
c) $x^2-5x-6=0$
d) $x^2-7x+6=0$
e) $x^2-x-20=0$
f) $x^2-x-\frac{63}{4}=0$
Question 10
Solve by completing the square
a) $x^2+3x+\frac{35}{16}=0$
b) $x^2-x+\frac{5}{36}=0$
c) $x^2-7x+\frac{187}{16}=0$
d) $x^2+9x+\frac{713}{36}=0$
e) $x^2-11x+\frac{2989}{100}=0$
f) $x^2-13x+\frac{3969}{100}=0$
Question 11
Solve by completing the square
a) $x^2+\frac32x+\frac12=0$
b) $x^2+\frac92x+2=0$
c) $x^2+\frac13x-\frac23=0$
d) $x^2-\frac53x-\frac{14}{9}=0$
e) $x^2-\frac65x-\frac{27}{25}=0$
f) $x^2-\frac75x-\frac{3}{20}=0$
Question 12
Solve. Remember there are two solutions
a) $x^2=2$
b) $x^2=6$
c) $x^2=11$
d) $x^2=8$
e) $x^2=18$
f) $x^2=45$
Question 13
Solve
a) $(x-2)^2=2$
b) $(x-7)^2=5$
c) $(x+3)^2-15=0$
d) $\left(x+\sqrt2\right)^2=2$
e) $\left(x-\sqrt3\right)^2=27$
f) $\left(x+2\sqrt7\right)^2-112$
Question 14
Solve by completing the square
a) $x^2+6x+7=0$
b) $x^2-4x+1=0$
c) $x^2+14x+39=0$
d) $x^2-2x-5=0$
e) $x^2-10x+17=0$
f) $x^2+16x-11=0$
Question 15
Solve by completing the square
a) $x^2+5x+\frac{11}{2}=0$
b) $x^2+x-1=0$
c) $x^2-7x+\frac{19}{2}=0$
d) $x^2-x+\frac{1}{36}=0$
e) $x^2-\frac52x+\frac54=0$
f) $x^2+\frac56x-\frac{1103}{225}=0$
Question 16
Solve by completing the square
a) $x^2+2\sqrt2x-6=0$
b) $x^2-2\sqrt3x-105=0$
c) $x^2-4\sqrt5x+15=0$
d) $x^2-\sqrt{72}x-14=0$
e) $x^2-\sqrt{2}x-\frac14=0$
f) $x^2+\sqrt5x+\frac{117}{100}=0$
Question 17
Solve by completing the square
a) $x^2=16-6x$
b) $y^2-39=10y$
c) $x(2x+1)=x^2+78\frac34-2x$
d) $x+5+\frac{9}{4x}=0$
e) $x^2\left(\frac12+\frac{\sqrt5}{x}\right)=20$
f) $1=\frac{17-8z\sqrt3}{16z^2}$
Answers
Question 1
a) $x=3$ or $x=-3$
b) $x=4$ or $x=-4$
c) $x=7$ or $x=-7$
d) $x=9$ or $x=-9$
e) $x=11$ or $x=-11$
f) $x=20$ or $x=-20$
Question 2
a) $x=5$
b) $x=8$
c) $x=-3$
d) $x=-7$
e) $x=12$
f) $x=-67$
Question 3
a) $x=-3$
b) $x=-5$
c) $x=-8$
d) $x=3$
e) $x=1$
f) $x=10$
Question 4
a) $x=7$ or $x=-3$
b) $x=11$ or $x=-1$
c) $x=18$ or $x=0$
d) $x=9$ or $x=-11$
e) $x=0$ or $x=-14$
f) $x=-2$ or $x=-26$
Question 5
a) $x=1$ or $x=-9$
b) $x=2$ or $x=-14$
c) $x=-8$ or $x=-14$
d) $x=1$ or $x=3$
e) $x=17$ or $x=-3$
f) $x=5$ or $x=19$
Question 6
a) $x=-3$ or $x=-7$
b) $x=-2$ or $x=-4$
c) $x=-3$ or $x=-13$
d) $x=19$ or $x=-1$
e) $x=-7$ or $x=9$
f) $x=-1$ or $x=23$
Question 7
a) $x=\frac13$ or $x=-\frac13$
b) $x=\frac15$ or $x=-\frac15$
c) $x=\frac12$ or $x=-\frac12$
d) $x=\frac34$ or $x=-\frac34$
e) $x=\frac58$ or $x=-\frac58$
f) $x=\frac{11}{7}$ or $x=-\frac{11}{7}$
Question 8
a) $x=-\frac23$ or $x=-\frac43$
b) $x=\frac{18}{5}$ or $x=\frac{22}{5}$
c) $x=\frac14$ or $x=-\frac54$
d) $x=-\frac{11}{6}$ or $x=-\frac{13}{6}$
e) $x=\frac57$ or $x=\frac97$
f) $x=-\frac79$ or $x=-\frac59$
Question 9
a) $x=1$ or $x=-4$
b) $x=1$ or $x=-2$
c) $x=-1$ or $x=6$
d) $x=1$ or $x=6$
e) $x=5$ or $x=-4$
f) $x=\frac92$ or $x=-\frac72$
Question 10
a) $x=-\frac74$ or $x=-\frac54$
b) $x=\frac16$ or $x=\frac56$
c) $x=\frac{11}{4}$ or $x=\frac{17}{4}$
d) $x=-\frac{31}{6}$ or $x=-\frac{23}{6}$
e) $x=\frac{49}{10}$ or $x=\frac{61}{10}$
f) $x=\frac{49}{10}$ or $x=\frac{81}{10}$
Question 11
a) $x=-1$ or $x=-\frac12$
b) $x=-4$ or $x=-\frac12$
c) $x=-1$ or $x=\frac23$
d) $x=-\frac23$ or $x=\frac73$
e) $x=\frac95$ or $x=-\frac35$
f) $x=\frac32$ or $x=-\frac{1}{10}$
Question 12
a) $x=\pm\sqrt2$
b) $x=\pm\sqrt6$
c) $x=\pm\sqrt{11}$
d) $x=\pm\sqrt8$ or $x=\pm2\sqrt2$
e) $x=\pm\sqrt{12}$ or $x=\pm2\sqrt3$
f) $x=\pm\sqrt{45}$ or $x=\pm3\sqrt5$
Question 13
a) $x=2\pm\sqrt2$
b) $x=7\pm\sqrt5$
c) $x=-3\pm\sqrt{15}$
d) $x=0$ or $x=-2\sqrt2$
e) $x=4\sqrt3$ or $x=-2\sqrt3$
f) $x=2\sqrt7$ or $x=-6\sqrt7$
Question 14
a) $x=-3\pm\sqrt2$
b) $x=2\pm\sqrt3$
c) $x=-7\pm\sqrt{10}$
d) $x=1\pm\sqrt6$
e) $x=5\pm2\sqrt2$
f) $x=-8\pm5\sqrt3$
Question 15
a) $x=\frac{-5\pm\sqrt3}{2}$
b) $x=\frac{-1\pm\sqrt5}{2}$
c) $x=\frac{7\pm\sqrt{11}}{2}$
d) $x=\frac12\pm\frac{\sqrt2}{3}$
or
$x=\frac{3\pm2\sqrt{2}}{6}$
e) $x=\frac{5\pm\sqrt{5}}{4}$
f) $x=\frac53\pm\frac{8\sqrt3}{5}$
or
$x=\frac{25\pm24\sqrt{3}}{15}$
Question 16
a) $x=\sqrt2$ or $x=-3\sqrt2$
b) $x=7\sqrt3$ or $x=-5\sqrt3$
c) $x=\sqrt5$ or $x=3\sqrt5$
d) $x=-\sqrt2$ or $x=7\sqrt2$
e) $x=\frac{\sqrt2\pm\sqrt3}{2}$
f) $x=-\frac{\sqrt5}{2}\pm\frac{\sqrt2}{5}$
or
$x=\frac{-5\sqrt5\pm2\sqrt2}{10}$
Question 17
a) $x=2$ or $x=-8$
b) $y=13$ or $y=-3$
c) $x=\frac{15}{2}$ or $x=-\frac{21}{2}$
d) $x=-\frac12$ or $x=-\frac92$
e) $x=2\sqrt5$ or $x=-4\sqrt5$
f) $z=\frac{-\sqrt3\pm2\sqrt5}{4}$