Algebra - Solving Non-Monic Quadratics by Completing the Square
Question 1
Solve. Remember there are two solutions
a) $2x^2=50$
a
$x=5$ or $x=-5$
Question ID: 20300010010
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b) $3x^2=27$
a
$x=3$ or $x=-3$
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c) $7x^2=112$
a
$x=4$ or $x=-4$
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d) $\frac12x^2=2$
a
$x=2$ or $x=-2$
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e) $0.4x^2=0.4$
a
$x=1$ or $x=-1$
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f) $\frac{245}{x^2}=5$
a
$x=7$ or $x=-7$
Question ID: 20300010060
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Question 2
Solve
a) $3(x-1)^2=0$
a
$x=1$
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b) $5(x-11)^2=0$
a
$x=11$
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c) $\frac14(x+9)^2=0$
a
$x=-9$
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d) $9(x+2.3)^2=0$
a
$x=-2.3$
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e) $(2x-8)^2=0$
a
$x=4$
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f) $\frac37(4x+11)^2=0$
a
$x=-\frac{11}{4}$
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Question 3
Solve, by taking out a common factor
a) $2x^2+16x+32=0$
a
$x=-4$
Question ID: 20300030010
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b) $3x^2+42x+147=0$
a
$x=-7$
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c) $5x^2-30x+45=0$
a
$x=3$
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d) $\frac12x^2-6x+18=0$
a
$x=6$
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e) $x^3+2x^2+x=0$
a
$x=1$ or $x=0$
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f) $0.1x^4-2x^3+x^2=0$
a
$x=10$ or $x=0$
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Question 4
Solve. Remember there are two solutions
a) $2(x-1)^2=50$
a
$x=6$ or $x=-4$
Question ID: 20300040010
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b) $3(x-2)^2=12$
a
$x=4$ or $x=0$
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c) $8(x+8)^2=800$
a
$x=2$ or $x=-18$
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d) $0.8(x+1)^2=51.2$
a
$x=7$ or $x=-9$
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e) $\frac14(x+15)^2=36$
a
$x=-3$ or $x=-27$
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f) $\frac37(x-54)^2=21$
a
$x=61$ or $x=47$
Question ID: 20300040060
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Question 5
Solve by completing the square on the left hand side
a) $2x^2+12x+18=32$
a
$x=1$ or $x=-7$
Question ID: 20300050010
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b) $4x^2-40x+100=16$
a
$x=7$ or $x=3$
Question ID: 20300050020
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c) $\frac12x^2-8x+32=50$
a
$x=18$ or $x=-2$
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d) $4x^2-80x+400=1$
a
$x=\frac{21}{2}$ or $x=\frac{19}{2}$
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e) $x^2+2x+1=0.36$
a
$x=-\frac25$ or $x=-\frac85$
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f) $0.8x^2-9.6x+28.8=5$
a
$x=\frac{17}{2}$ or $x=\frac72$
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Question 6
Solve by completing the square
a) $2x^2+4x-48=0$
a
$x=4$ or $x=-6$
Question ID: 20300060010
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b) $3x^2+30x+72=0$
a
$x=-4$ or $x=-6$
Question ID: 20300060020
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c) $5x^2-20x=0$
a
$x=4$ or $x=0$
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d) $4x^2-56x+160=0$
a
$x=10$ or $x=4$
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e) $7x^2+42x-189=0$
a
$x=3$ or $x=-9$
Question ID: 20300060050
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f) $9x^2-126x-288=0$
a
$x=16$ or $x=-2$
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Question 7
Solve by completing the square
a) $2x^2-12x+\frac{35}{2}=0$
a
$x=\frac72$ or $x=\frac52$
Question ID: 20300070010
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b) $3x^2-6x+\frac83=0$
a
$x=\frac43$ or $x=\frac23$
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c) $2x^2+12x+17\frac79=0$
a
$x=-\frac83$ or $x=-\frac{10}{3}$
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d) $4x^2-24x+\frac{224}{9}=0$
a
$x=\frac{14}{3}$ or $x=\frac{4}{3}$
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e) $5x^2+50x+124\frac{19}{20}=0$
a
$x=-\frac{49}{10}$ or $x=-\frac{51}{10}$
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f) $8x^2-48x+60\frac{12}{25}=0$
a
$x=\frac{21}{5}$ or $x=\frac95$
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Question 8
Solve
a) $3\left(x+\frac12\right)^2=\frac34$
a
$x=0$ or $x=-1$
Question ID: 20300080010
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b) $5\left(x-\frac25\right)^2=\frac15$
a
$x=\frac35$ or $x=\frac15$
Question ID: 20300080020
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c) $2\left(x+\frac14\right)^2=1\frac{1}{8}$
a
$x=\frac12$ or $x=-1$
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d) $8\left(x-\frac67\right)^2=\frac{32}{49}$
a
$x=\frac47$ or $x=\frac87$
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e) $\frac12\left(x+3.5\right)^2=\frac{25}{8}$
a
$x=-1$ or $x=-6$
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f) $\frac37\left(x-1\frac16\right)^2=\frac{27}{28}$
a
$x=\frac83$ or $x=-\frac13$
Question ID: 20300080060
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Question 9
Solve by completing the square on the left hand side
a) $2x^2-2x+\frac12=2$
a
$x=\frac32$ or $x=-\frac12$
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b) $5x^2+2x+\frac15=20$
a
$x=\frac95$ or $x=-\frac{11}{5}$
Question ID: 20300090020
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c) $9x^2-12x+4=81$
a
$x=\frac{11}{3}$ or $x=-\frac73$
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d) $\frac12x^2+4x+8=8$
a
$x=0$ or $x=-8$
Question ID: 20300090040
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e) $\frac13x^2-\frac13x+\frac{1}{12}=27$
a
$x=\frac{19}{2}$ or $x=-\frac{17}{2}$
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f) $112x^2-168x+63=448$
a
$x=\frac{11}{4}$ or $x=-\frac54$
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Question 10
Solve by completing the square
a) $8x^2-8x-70=0$
a
$x=\frac72$ or $x=-\frac52$
Question ID: 20300100010
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b) $4x^2+20x+21=0$
a
$x=-\frac32$ or $x=-\frac72$
Question ID: 20300100020
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c) $20x^2-60x-35=0$
a
$x=\frac72$ or $x=-\frac12$
Question ID: 20300100030
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d) $2x^2+2x-\frac{35}{2}=0$
a
$x=\frac52$ or $x=-\frac72$
Question ID: 20300100040
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e) $3x^2-9x-\frac{21}{4}=0$
a
$x=\frac72$ or $x=-\frac12$
Question ID: 20300100050
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f) $\frac12x^2+\frac54x-\frac{119}{32}=0$
a
$x=\frac74$ or $x=-\frac{17}{4}$
Question ID: 20300100060
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click hereQuestion by: ada
Answer by: ada
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Question ID: 20300100060
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Question ID: 20300100060
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Question 1
Solve. Remember there are two solutions
a) $2x^2=50$
b) $3x^2=27$
c) $7x^2=112$
d) $\frac12x^2=2$
e) $0.4x^2=0.4$
f) $\frac{245}{x^2}=5$
Question 2
Solve
a) $3(x-1)^2=0$
b) $5(x-11)^2=0$
c) $\frac14(x+9)^2=0$
d) $9(x+2.3)^2=0$
e) $(2x-8)^2=0$
f) $\frac37(4x+11)^2=0$
Question 3
Solve, by taking out a common factor
a) $2x^2+16x+32=0$
b) $3x^2+42x+147=0$
c) $5x^2-30x+45=0$
d) $\frac12x^2-6x+18=0$
e) $x^3+2x^2+x=0$
f) $0.1x^4-2x^3+x^2=0$
Question 4
Solve. Remember there are two solutions
a) $2(x-1)^2=50$
b) $3(x-2)^2=12$
c) $8(x+8)^2=800$
d) $0.8(x+1)^2=51.2$
e) $\frac14(x+15)^2=36$
f) $\frac37(x-54)^2=21$
Question 5
Solve by completing the square on the left hand side
a) $2x^2+12x+18=32$
b) $4x^2-40x+100=16$
c) $\frac12x^2-8x+32=50$
d) $4x^2-80x+400=1$
e) $x^2+2x+1=0.36$
f) $0.8x^2-9.6x+28.8=5$
Question 6
Solve by completing the square
a) $2x^2+4x-48=0$
b) $3x^2+30x+72=0$
c) $5x^2-20x=0$
d) $4x^2-56x+160=0$
e) $7x^2+42x-189=0$
f) $9x^2-126x-288=0$
Question 7
Solve by completing the square
a) $2x^2-12x+\frac{35}{2}=0$
b) $3x^2-6x+\frac83=0$
c) $2x^2+12x+17\frac79=0$
d) $4x^2-24x+\frac{224}{9}=0$
e) $5x^2+50x+124\frac{19}{20}=0$
f) $8x^2-48x+60\frac{12}{25}=0$
Question 8
Solve
a) $3\left(x+\frac12\right)^2=\frac34$
b) $5\left(x-\frac25\right)^2=\frac15$
c) $2\left(x+\frac14\right)^2=1\frac{1}{8}$
d) $8\left(x-\frac67\right)^2=\frac{32}{49}$
e) $\frac12\left(x+3.5\right)^2=\frac{25}{8}$
f) $\frac37\left(x-1\frac16\right)^2=\frac{27}{28}$
Question 9
Solve by completing the square on the left hand side
a) $2x^2-2x+\frac12=2$
b) $5x^2+2x+\frac15=20$
c) $9x^2-12x+4=81$
d) $\frac12x^2+4x+8=8$
e) $\frac13x^2-\frac13x+\frac{1}{12}=27$
f) $112x^2-168x+63=448$
Question 10
Solve by completing the square
a) $8x^2-8x-70=0$
b) $4x^2+20x+21=0$
c) $20x^2-60x-35=0$
d) $2x^2+2x-\frac{35}{2}=0$
e) $3x^2-9x-\frac{21}{4}=0$
f) $\frac12x^2+\frac54x-\frac{119}{32}=0$
Answers
Question 1
a) $x=5$ or $x=-5$
b) $x=3$ or $x=-3$
c) $x=4$ or $x=-4$
d) $x=2$ or $x=-2$
e) $x=1$ or $x=-1$
f) $x=7$ or $x=-7$
Question 2
a) $x=1$
b) $x=11$
c) $x=-9$
d) $x=-2.3$
e) $x=4$
f) $x=-\frac{11}{4}$
Question 3
a) $x=-4$
b) $x=-7$
c) $x=3$
d) $x=6$
e) $x=1$ or $x=0$
f) $x=10$ or $x=0$
Question 4
a) $x=6$ or $x=-4$
b) $x=4$ or $x=0$
c) $x=2$ or $x=-18$
d) $x=7$ or $x=-9$
e) $x=-3$ or $x=-27$
f) $x=61$ or $x=47$
Question 5
a) $x=1$ or $x=-7$
b) $x=7$ or $x=3$
c) $x=18$ or $x=-2$
d) $x=\frac{21}{2}$ or $x=\frac{19}{2}$
e) $x=-\frac25$ or $x=-\frac85$
f) $x=\frac{17}{2}$ or $x=\frac72$
Question 6
a) $x=4$ or $x=-6$
b) $x=-4$ or $x=-6$
c) $x=4$ or $x=0$
d) $x=10$ or $x=4$
e) $x=3$ or $x=-9$
f) $x=16$ or $x=-2$
Question 7
a) $x=\frac72$ or $x=\frac52$
b) $x=\frac43$ or $x=\frac23$
c) $x=-\frac83$ or $x=-\frac{10}{3}$
d) $x=\frac{14}{3}$ or $x=\frac{4}{3}$
e) $x=-\frac{49}{10}$ or $x=-\frac{51}{10}$
f) $x=\frac{21}{5}$ or $x=\frac95$
Question 8
a) $x=0$ or $x=-1$
b) $x=\frac35$ or $x=\frac15$
c) $x=\frac12$ or $x=-1$
d) $x=\frac47$ or $x=\frac87$
e) $x=-1$ or $x=-6$
f) $x=\frac83$ or $x=-\frac13$
Question 9
a) $x=\frac32$ or $x=-\frac12$
b) $x=\frac95$ or $x=-\frac{11}{5}$
c) $x=\frac{11}{3}$ or $x=-\frac73$
d) $x=0$ or $x=-8$
e) $x=\frac{19}{2}$ or $x=-\frac{17}{2}$
f) $x=\frac{11}{4}$ or $x=-\frac54$
Question 10
a) $x=\frac72$ or $x=-\frac52$
b) $x=-\frac32$ or $x=-\frac72$
c) $x=\frac72$ or $x=-\frac12$
d) $x=\frac52$ or $x=-\frac72$
e) $x=\frac72$ or $x=-\frac12$
f) $x=\frac74$ or $x=-\frac{17}{4}$
Question 1
Solve. Remember there are two solutions
a) $2x^2=50$
b) $3x^2=27$
c) $7x^2=112$
d) $\frac12x^2=2$
e) $0.4x^2=0.4$
f) $\frac{245}{x^2}=5$
Question 2
Solve
a) $3(x-1)^2=0$
b) $5(x-11)^2=0$
c) $\frac14(x+9)^2=0$
d) $9(x+2.3)^2=0$
e) $(2x-8)^2=0$
f) $\frac37(4x+11)^2=0$
Question 3
Solve, by taking out a common factor
a) $2x^2+16x+32=0$
b) $3x^2+42x+147=0$
c) $5x^2-30x+45=0$
d) $\frac12x^2-6x+18=0$
e) $x^3+2x^2+x=0$
f) $0.1x^4-2x^3+x^2=0$
Question 4
Solve. Remember there are two solutions
a) $2(x-1)^2=50$
b) $3(x-2)^2=12$
c) $8(x+8)^2=800$
d) $0.8(x+1)^2=51.2$
e) $\frac14(x+15)^2=36$
f) $\frac37(x-54)^2=21$
Question 5
Solve by completing the square on the left hand side
a) $2x^2+12x+18=32$
b) $4x^2-40x+100=16$
c) $\frac12x^2-8x+32=50$
d) $4x^2-80x+400=1$
e) $x^2+2x+1=0.36$
f) $0.8x^2-9.6x+28.8=5$
Question 6
Solve by completing the square
a) $2x^2+4x-48=0$
b) $3x^2+30x+72=0$
c) $5x^2-20x=0$
d) $4x^2-56x+160=0$
e) $7x^2+42x-189=0$
f) $9x^2-126x-288=0$
Question 7
Solve by completing the square
a) $2x^2-12x+\frac{35}{2}=0$
b) $3x^2-6x+\frac83=0$
c) $2x^2+12x+17\frac79=0$
d) $4x^2-24x+\frac{224}{9}=0$
e) $5x^2+50x+124\frac{19}{20}=0$
f) $8x^2-48x+60\frac{12}{25}=0$
Question 8
Solve
a) $3\left(x+\frac12\right)^2=\frac34$
b) $5\left(x-\frac25\right)^2=\frac15$
c) $2\left(x+\frac14\right)^2=1\frac{1}{8}$
d) $8\left(x-\frac67\right)^2=\frac{32}{49}$
e) $\frac12\left(x+3.5\right)^2=\frac{25}{8}$
f) $\frac37\left(x-1\frac16\right)^2=\frac{27}{28}$
Question 9
Solve by completing the square on the left hand side
a) $2x^2-2x+\frac12=2$
b) $5x^2+2x+\frac15=20$
c) $9x^2-12x+4=81$
d) $\frac12x^2+4x+8=8$
e) $\frac13x^2-\frac13x+\frac{1}{12}=27$
f) $112x^2-168x+63=448$
Question 10
Solve by completing the square
a) $8x^2-8x-70=0$
b) $4x^2+20x+21=0$
c) $20x^2-60x-35=0$
d) $2x^2+2x-\frac{35}{2}=0$
e) $3x^2-9x-\frac{21}{4}=0$
f) $\frac12x^2+\frac54x-\frac{119}{32}=0$
Answers
Question 1
a) $x=5$ or $x=-5$
b) $x=3$ or $x=-3$
c) $x=4$ or $x=-4$
d) $x=2$ or $x=-2$
e) $x=1$ or $x=-1$
f) $x=7$ or $x=-7$
Question 2
a) $x=1$
b) $x=11$
c) $x=-9$
d) $x=-2.3$
e) $x=4$
f) $x=-\frac{11}{4}$
Question 3
a) $x=-4$
b) $x=-7$
c) $x=3$
d) $x=6$
e) $x=1$ or $x=0$
f) $x=10$ or $x=0$
Question 4
a) $x=6$ or $x=-4$
b) $x=4$ or $x=0$
c) $x=2$ or $x=-18$
d) $x=7$ or $x=-9$
e) $x=-3$ or $x=-27$
f) $x=61$ or $x=47$
Question 5
a) $x=1$ or $x=-7$
b) $x=7$ or $x=3$
c) $x=18$ or $x=-2$
d) $x=\frac{21}{2}$ or $x=\frac{19}{2}$
e) $x=-\frac25$ or $x=-\frac85$
f) $x=\frac{17}{2}$ or $x=\frac72$
Question 6
a) $x=4$ or $x=-6$
b) $x=-4$ or $x=-6$
c) $x=4$ or $x=0$
d) $x=10$ or $x=4$
e) $x=3$ or $x=-9$
f) $x=16$ or $x=-2$
Question 7
a) $x=\frac72$ or $x=\frac52$
b) $x=\frac43$ or $x=\frac23$
c) $x=-\frac83$ or $x=-\frac{10}{3}$
d) $x=\frac{14}{3}$ or $x=\frac{4}{3}$
e) $x=-\frac{49}{10}$ or $x=-\frac{51}{10}$
f) $x=\frac{21}{5}$ or $x=\frac95$
Question 8
a) $x=0$ or $x=-1$
b) $x=\frac35$ or $x=\frac15$
c) $x=\frac12$ or $x=-1$
d) $x=\frac47$ or $x=\frac87$
e) $x=-1$ or $x=-6$
f) $x=\frac83$ or $x=-\frac13$
Question 9
a) $x=\frac32$ or $x=-\frac12$
b) $x=\frac95$ or $x=-\frac{11}{5}$
c) $x=\frac{11}{3}$ or $x=-\frac73$
d) $x=0$ or $x=-8$
e) $x=\frac{19}{2}$ or $x=-\frac{17}{2}$
f) $x=\frac{11}{4}$ or $x=-\frac54$
Question 10
a) $x=\frac72$ or $x=-\frac52$
b) $x=-\frac32$ or $x=-\frac72$
c) $x=\frac72$ or $x=-\frac12$
d) $x=\frac52$ or $x=-\frac72$
e) $x=\frac72$ or $x=-\frac12$
f) $x=\frac74$ or $x=-\frac{17}{4}$
Solutions
Question 1
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b)
c)
d)
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f)
Question 2
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c)
d)
e)
f)
Question 3
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Question 4
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Question 5
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Question 6
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Question 7
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Question 8
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Question 9
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Question 10
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