Algebra - Completing the Square on Monic Expressions
Question 1
What number should be added in order to form a perfect square?
a) $x^2+2x+\square$
a
$1$
Question ID: 20170010010
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b) $x^2+4x+\square$
a
$2$
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c) $x^2+10x+\square$
a
$25$
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d) $x^2+20x+\square$
a
$100$
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e) $x^2+8x+\square$
a
$16$
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f) $x^2+12x+\square$
a
$36$
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g) $x^2+22x+\square$
a
$121$
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h) $x^2+30x+\square$
a
$225$
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Question 2
What number should be added in order to form a perfect square? Leave answers as top-heavy/improper fractions where necessary
a) $x^2+3x+\square$
a
$\frac94$
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b) $x^2+5x+\square$
a
$\frac{25}{4}$
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c) $x^2+9x+\square$
a
$\frac{81}{4}$
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d) $x^2+7x+\square$
a
$\frac{49}{4}$
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e) $x^2+x+\square$
a
$\frac{1}{4}$
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f) $x^2+11x+\square$
a
$\frac{121}{4}$
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g) $x^2+13x+\square$
a
$\frac{169}{4}$
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h) $x^2+15x+\square$
a
$\frac{225}{4}$
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Question 3
What number should be added in order to form a perfect square? Leave answers as top-heavy/improper fractions where necessary
a) $x^2-2x+\square$
a
$1$
Question ID: 20170030010
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b) $x^2-4x+\square$
a
$4$
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c) $x^2-8x+\square$
a
$16$
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d) $x^2-3x+\square$
a
$\frac94$
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e) $x^2-7x+\square$
a
$\frac{49}{4}$
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f) $x^2-11x+\square$
a
$\frac{121}{4}$
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g) $x^2-18x+\square$
a
$81$
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h) $x^2-13x+\square$
a
$\frac{169}{4}$
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Question 4
Complete the square
a) $x^2+4x+5$
a
${\left(x+2\right)}^2+1$
Question ID: 20170040010
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b) $x^2+6x+10$
a
${\left(x+3\right)}^2+1$
Question ID: 20170040020
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c) $x^2+10x+28$
a
${\left(x+5\right)}^2+3$
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d) $x^2+16x+70$
a
${\left(x+8\right)}^2+6$
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e) $x^2+20x+120$
a
${\left(x+10\right)}^2+20$
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f) $x^2+8x+16$
a
${\left(x+4\right)}^2$
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g) $x^2+12x+50$
a
${\left(x+6\right)}^2+14$
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h) $x^2+18x+110$
a
${\left(x+9\right)}^2+29$
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Question 5
Complete the square
a) $x^2+6x+8$
a
${\left(x+3\right)}^2-1$
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b) $x^2+8x+12$
a
${\left(x+4\right)}^2-4$
Question ID: 20170050020
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c) $x^2+12x+33$
a
${\left(x+6\right)}^2-3$
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d) $x^2+14x+39$
a
${\left(x+7\right)}^2-10$
Question ID: 20170050040
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e) $x^2+10x+12$
a
${\left(x+5\right)}^2-13$
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f) $x^2+16x+64$
a
${\left(x+8\right)}^2$
Question ID: 20170050060
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g) $x^2+2x-1$
a
${\left(x+1\right)}^2-2$
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h) $x^2+18x-219$
a
${\left(x+9\right)}^2-300$
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Question 6
Complete the square
a) $x^2-6x+11$
a
${\left(x-3\right)}^2+2$
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b) $x^2-10x+29$
a
${\left(x-5\right)}^2+4$
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c) $x^2-8x+26$
a
${\left(x-4\right)}^2+10$
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d) $x^2-18x+114$
a
${\left(x-9\right)}^2+33$
Question ID: 20170060040
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e) $x^2-22x+138$
a
${\left(x-11\right)}^2+17$
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f) $x^2-4x+1$
a
${\left(x-2\right)}^2-3$
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g) $x^2-2x-5$
a
${\left(x-1\right)}^2-4$
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h) $x^2-22x+76$
a
${\left(x-11\right)}^2-45$
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Question 7
Complete the square. Leave answers as top-heavy/improper fractions where necessary
a) $x^2+3x+3$
a
${\left(x+\frac32\right)}^2+\frac34$
Question ID: 20170070010
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b) $x^2+5x+7$
a
${\left(x+\frac52\right)}^2+\frac34$
Question ID: 20170070020
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c) $x^2+9x+20$
a
${\left(x+\frac92\right)}^2-\frac14$
Question ID: 20170070030
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d) $x^2+x+5$
a
${\left(x+\frac12\right)}^2+\frac{19}{4}$
Question ID: 20170070040
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e) $x^2+7x+10$
a
${\left(x+\frac72\right)}^2-\frac{9}{4}$
Question ID: 20170070050
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f) $x^2+11x+25$
a
${\left(x+\frac{11}{2}\right)}^2-\frac{21}{4}$
Question ID: 20170070060
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g) $x^2+3x-4$
a
${\left(x+\frac{3}{2}\right)}^2-\frac{25}{4}$
Question ID: 20170070070
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h) $x^2+9x-\frac34$
a
${\left(x+\frac{9}{2}\right)}^2-\frac{3}{4}$
Question ID: 20170070080
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Question 8
Complete the square. Leave answers as top-heavy/improper fractions where necessary
a) $x^2-3x+4$
a
${\left(x-\frac32\right)}^2+\frac74$
Question ID: 20170080010
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b) $x^2-7x+10$
a
${\left(x-\frac72\right)}^2-\frac94$
Question ID: 20170080020
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c) $x^2-5x+2$
a
${\left(x-\frac52\right)}^2-\frac{17}{4}$
Question ID: 20170080030
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d) $x^2-x+7$
a
${\left(x-\frac12\right)}^2+\frac74$
Question ID: 20170080040
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e) $x^2-11x$
a
${\left(x-\frac{11}{2}\right)}^2-\frac{121}{4}$
Question ID: 20170080050
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f) $x^2-3x+\frac34$
a
${\left(x-\frac32\right)}^2-\frac32$
Question ID: 20170080060
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g) $x^2-5x-\frac58$
a
${\left(x-\frac52\right)}^2-\frac{55}{8}$
Question ID: 20170080070
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h) $x^2-13x+12.5$
a
${\left(x-\frac{13}{2}\right)}^2+\frac{119}{4}$
Question ID: 20170080080
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Question 9
Complete the square
a) $x^2+\frac12x+1$
a
${\left(x+\frac14\right)}^2+\frac{15}{16}$
Question ID: 20170090010
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b) $x^2+\frac43x$
a
${\left(x+\frac23\right)}^2-\frac49$
Question ID: 20170090020
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c) $x^2-\frac74x+15$
a
${\left(x-\frac78\right)}^2+\frac{79}{64}$
Question ID: 20170090030
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d) $x^2+0.2x+1$
a
${\left(x+0.1\right)}^2+0.99$
Question ID: 20170090040
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e) $x^2+1.2x-2$
a
${\left(x+0.6\right)}^2-2.36$
Question ID: 20170090050
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f) $x^2-0.3x+0.5$
a
${\left(x+0.15\right)}^2+0.4775$
Question ID: 20170090060
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g) $x^4-2x^2+5$
a
${\left(x^2-1\right)}^2+4$
Question ID: 20170090070
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h) $x^6+\frac14x^3-\frac45$
a
${\left(x^3+\frac18\right)}^2-\frac{261}{320}$
Question ID: 20170090080
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Question 1
What number should be added in order to form a perfect square?
a) $x^2+2x+\square$
b) $x^2+4x+\square$
c) $x^2+10x+\square$
d) $x^2+20x+\square$
e) $x^2+8x+\square$
f) $x^2+12x+\square$
g) $x^2+22x+\square$
h) $x^2+30x+\square$
Question 2
What number should be added in order to form a perfect square? Leave answers as top-heavy/improper fractions where necessary
a) $x^2+3x+\square$
b) $x^2+5x+\square$
c) $x^2+9x+\square$
d) $x^2+7x+\square$
e) $x^2+x+\square$
f) $x^2+11x+\square$
g) $x^2+13x+\square$
h) $x^2+15x+\square$
Question 3
What number should be added in order to form a perfect square? Leave answers as top-heavy/improper fractions where necessary
a) $x^2-2x+\square$
b) $x^2-4x+\square$
c) $x^2-8x+\square$
d) $x^2-3x+\square$
e) $x^2-7x+\square$
f) $x^2-11x+\square$
g) $x^2-18x+\square$
h) $x^2-13x+\square$
Question 4
Complete the square
a) $x^2+4x+5$
b) $x^2+6x+10$
c) $x^2+10x+28$
d) $x^2+16x+70$
e) $x^2+20x+120$
f) $x^2+8x+16$
g) $x^2+12x+50$
h) $x^2+18x+110$
Question 5
Complete the square
a) $x^2+6x+8$
b) $x^2+8x+12$
c) $x^2+12x+33$
d) $x^2+14x+39$
e) $x^2+10x+12$
f) $x^2+16x+64$
g) $x^2+2x-1$
h) $x^2+18x-219$
Question 6
Complete the square
a) $x^2-6x+11$
b) $x^2-10x+29$
c) $x^2-8x+26$
d) $x^2-18x+114$
e) $x^2-22x+138$
f) $x^2-4x+1$
g) $x^2-2x-5$
h) $x^2-22x+76$
Question 7
Complete the square. Leave answers as top-heavy/improper fractions where necessary
a) $x^2+3x+3$
b) $x^2+5x+7$
c) $x^2+9x+20$
d) $x^2+x+5$
e) $x^2+7x+10$
f) $x^2+11x+25$
g) $x^2+3x-4$
h) $x^2+9x-\frac34$
Question 8
Complete the square. Leave answers as top-heavy/improper fractions where necessary
a) $x^2-3x+4$
b) $x^2-7x+10$
c) $x^2-5x+2$
d) $x^2-x+7$
e) $x^2-11x$
f) $x^2-3x+\frac34$
g) $x^2-5x-\frac58$
h) $x^2-13x+12.5$
Question 9
Complete the square
a) $x^2+\frac12x+1$
b) $x^2+\frac43x$
c) $x^2-\frac74x+15$
d) $x^2+0.2x+1$
e) $x^2+1.2x-2$
f) $x^2-0.3x+0.5$
g) $x^4-2x^2+5$
h) $x^6+\frac14x^3-\frac45$
Answers
Question 1
a) $1$
b) $2$
c) $25$
d) $100$
e) $16$
f) $36$
g) $121$
h) $225$
Question 2
a) $\frac94$
b) $\frac{25}{4}$
c) $\frac{81}{4}$
d) $\frac{49}{4}$
e) $\frac{1}{4}$
f) $\frac{121}{4}$
g) $\frac{169}{4}$
h) $\frac{225}{4}$
Question 3
a) $1$
b) $4$
c) $16$
d) $\frac94$
e) $\frac{49}{4}$
f) $\frac{121}{4}$
g) $81$
h) $\frac{169}{4}$
Question 4
a) ${\left(x+2\right)}^2+1$
b) ${\left(x+3\right)}^2+1$
c) ${\left(x+5\right)}^2+3$
d) ${\left(x+8\right)}^2+6$
e) ${\left(x+10\right)}^2+20$
f) ${\left(x+4\right)}^2$
g) ${\left(x+6\right)}^2+14$
h) ${\left(x+9\right)}^2+29$
Question 5
a) ${\left(x+3\right)}^2-1$
b) ${\left(x+4\right)}^2-4$
c) ${\left(x+6\right)}^2-3$
d) ${\left(x+7\right)}^2-10$
e) ${\left(x+5\right)}^2-13$
f) ${\left(x+8\right)}^2$
g) ${\left(x+1\right)}^2-2$
h) ${\left(x+9\right)}^2-300$
Question 6
a) ${\left(x-3\right)}^2+2$
b) ${\left(x-5\right)}^2+4$
c) ${\left(x-4\right)}^2+10$
d) ${\left(x-9\right)}^2+33$
e) ${\left(x-11\right)}^2+17$
f) ${\left(x-2\right)}^2-3$
g) ${\left(x-1\right)}^2-4$
h) ${\left(x-11\right)}^2-45$
Question 7
a) ${\left(x+\frac32\right)}^2+\frac34$
b) ${\left(x+\frac52\right)}^2+\frac34$
c) ${\left(x+\frac92\right)}^2-\frac14$
d) ${\left(x+\frac12\right)}^2+\frac{19}{4}$
e) ${\left(x+\frac72\right)}^2-\frac{9}{4}$
f) ${\left(x+\frac{11}{2}\right)}^2-\frac{21}{4}$
g) ${\left(x+\frac{3}{2}\right)}^2-\frac{25}{4}$
h) ${\left(x+\frac{9}{2}\right)}^2-\frac{3}{4}$
Question 8
a) ${\left(x-\frac32\right)}^2+\frac74$
b) ${\left(x-\frac72\right)}^2-\frac94$
c) ${\left(x-\frac52\right)}^2-\frac{17}{4}$
d) ${\left(x-\frac12\right)}^2+\frac74$
e) ${\left(x-\frac{11}{2}\right)}^2-\frac{121}{4}$
f) ${\left(x-\frac32\right)}^2-\frac32$
g) ${\left(x-\frac52\right)}^2-\frac{55}{8}$
h) ${\left(x-\frac{13}{2}\right)}^2+\frac{119}{4}$
Question 9
a) ${\left(x+\frac14\right)}^2+\frac{15}{16}$
b) ${\left(x+\frac23\right)}^2-\frac49$
c) ${\left(x-\frac78\right)}^2+\frac{79}{64}$
d) ${\left(x+0.1\right)}^2+0.99$
e) ${\left(x+0.6\right)}^2-2.36$
f) ${\left(x+0.15\right)}^2+0.4775$
g) ${\left(x^2-1\right)}^2+4$
h) ${\left(x^3+\frac18\right)}^2-\frac{261}{320}$
Question 1
What number should be added in order to form a perfect square?
a) $x^2+2x+\square$
b) $x^2+4x+\square$
c) $x^2+10x+\square$
d) $x^2+20x+\square$
e) $x^2+8x+\square$
f) $x^2+12x+\square$
g) $x^2+22x+\square$
h) $x^2+30x+\square$
Question 2
What number should be added in order to form a perfect square? Leave answers as top-heavy/improper fractions where necessary
a) $x^2+3x+\square$
b) $x^2+5x+\square$
c) $x^2+9x+\square$
d) $x^2+7x+\square$
e) $x^2+x+\square$
f) $x^2+11x+\square$
g) $x^2+13x+\square$
h) $x^2+15x+\square$
Question 3
What number should be added in order to form a perfect square? Leave answers as top-heavy/improper fractions where necessary
a) $x^2-2x+\square$
b) $x^2-4x+\square$
c) $x^2-8x+\square$
d) $x^2-3x+\square$
e) $x^2-7x+\square$
f) $x^2-11x+\square$
g) $x^2-18x+\square$
h) $x^2-13x+\square$
Question 4
Complete the square
a) $x^2+4x+5$
b) $x^2+6x+10$
c) $x^2+10x+28$
d) $x^2+16x+70$
e) $x^2+20x+120$
f) $x^2+8x+16$
g) $x^2+12x+50$
h) $x^2+18x+110$
Question 5
Complete the square
a) $x^2+6x+8$
b) $x^2+8x+12$
c) $x^2+12x+33$
d) $x^2+14x+39$
e) $x^2+10x+12$
f) $x^2+16x+64$
g) $x^2+2x-1$
h) $x^2+18x-219$
Question 6
Complete the square
a) $x^2-6x+11$
b) $x^2-10x+29$
c) $x^2-8x+26$
d) $x^2-18x+114$
e) $x^2-22x+138$
f) $x^2-4x+1$
g) $x^2-2x-5$
h) $x^2-22x+76$
Question 7
Complete the square. Leave answers as top-heavy/improper fractions where necessary
a) $x^2+3x+3$
b) $x^2+5x+7$
c) $x^2+9x+20$
d) $x^2+x+5$
e) $x^2+7x+10$
f) $x^2+11x+25$
g) $x^2+3x-4$
h) $x^2+9x-\frac34$
Question 8
Complete the square. Leave answers as top-heavy/improper fractions where necessary
a) $x^2-3x+4$
b) $x^2-7x+10$
c) $x^2-5x+2$
d) $x^2-x+7$
e) $x^2-11x$
f) $x^2-3x+\frac34$
g) $x^2-5x-\frac58$
h) $x^2-13x+12.5$
Question 9
Complete the square
a) $x^2+\frac12x+1$
b) $x^2+\frac43x$
c) $x^2-\frac74x+15$
d) $x^2+0.2x+1$
e) $x^2+1.2x-2$
f) $x^2-0.3x+0.5$
g) $x^4-2x^2+5$
h) $x^6+\frac14x^3-\frac45$
Answers
Question 1
a) $1$
b) $2$
c) $25$
d) $100$
e) $16$
f) $36$
g) $121$
h) $225$
Question 2
a) $\frac94$
b) $\frac{25}{4}$
c) $\frac{81}{4}$
d) $\frac{49}{4}$
e) $\frac{1}{4}$
f) $\frac{121}{4}$
g) $\frac{169}{4}$
h) $\frac{225}{4}$
Question 3
a) $1$
b) $4$
c) $16$
d) $\frac94$
e) $\frac{49}{4}$
f) $\frac{121}{4}$
g) $81$
h) $\frac{169}{4}$
Question 4
a) ${\left(x+2\right)}^2+1$
b) ${\left(x+3\right)}^2+1$
c) ${\left(x+5\right)}^2+3$
d) ${\left(x+8\right)}^2+6$
e) ${\left(x+10\right)}^2+20$
f) ${\left(x+4\right)}^2$
g) ${\left(x+6\right)}^2+14$
h) ${\left(x+9\right)}^2+29$
Question 5
a) ${\left(x+3\right)}^2-1$
b) ${\left(x+4\right)}^2-4$
c) ${\left(x+6\right)}^2-3$
d) ${\left(x+7\right)}^2-10$
e) ${\left(x+5\right)}^2-13$
f) ${\left(x+8\right)}^2$
g) ${\left(x+1\right)}^2-2$
h) ${\left(x+9\right)}^2-300$
Question 6
a) ${\left(x-3\right)}^2+2$
b) ${\left(x-5\right)}^2+4$
c) ${\left(x-4\right)}^2+10$
d) ${\left(x-9\right)}^2+33$
e) ${\left(x-11\right)}^2+17$
f) ${\left(x-2\right)}^2-3$
g) ${\left(x-1\right)}^2-4$
h) ${\left(x-11\right)}^2-45$
Question 7
a) ${\left(x+\frac32\right)}^2+\frac34$
b) ${\left(x+\frac52\right)}^2+\frac34$
c) ${\left(x+\frac92\right)}^2-\frac14$
d) ${\left(x+\frac12\right)}^2+\frac{19}{4}$
e) ${\left(x+\frac72\right)}^2-\frac{9}{4}$
f) ${\left(x+\frac{11}{2}\right)}^2-\frac{21}{4}$
g) ${\left(x+\frac{3}{2}\right)}^2-\frac{25}{4}$
h) ${\left(x+\frac{9}{2}\right)}^2-\frac{3}{4}$
Question 8
a) ${\left(x-\frac32\right)}^2+\frac74$
b) ${\left(x-\frac72\right)}^2-\frac94$
c) ${\left(x-\frac52\right)}^2-\frac{17}{4}$
d) ${\left(x-\frac12\right)}^2+\frac74$
e) ${\left(x-\frac{11}{2}\right)}^2-\frac{121}{4}$
f) ${\left(x-\frac32\right)}^2-\frac32$
g) ${\left(x-\frac52\right)}^2-\frac{55}{8}$
h) ${\left(x-\frac{13}{2}\right)}^2+\frac{119}{4}$
Question 9
a) ${\left(x+\frac14\right)}^2+\frac{15}{16}$
b) ${\left(x+\frac23\right)}^2-\frac49$
c) ${\left(x-\frac78\right)}^2+\frac{79}{64}$
d) ${\left(x+0.1\right)}^2+0.99$
e) ${\left(x+0.6\right)}^2-2.36$
f) ${\left(x+0.15\right)}^2+0.4775$
g) ${\left(x^2-1\right)}^2+4$
h) ${\left(x^3+\frac18\right)}^2-\frac{261}{320}$
Solutions
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Question 8
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Question 9
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