# 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
$25$

Question ID: 20170010030

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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
$\frac94$

Question ID: 20170020010

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b) $x^2+5x+\square$

a
$\frac{25}{4}$

Question ID: 20170020020

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c) $x^2+9x+\square$

a
$\frac{81}{4}$

Question ID: 20170020030

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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
$\frac{121}{4}$

Question ID: 20170020060

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g) $x^2+13x+\square$

a
$\frac{169}{4}$

Question ID: 20170020070

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h) $x^2+15x+\square$

a
$\frac{225}{4}$

Question ID: 20170020080

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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
$16$

Question ID: 20170030030

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d) $x^2-3x+\square$

a
$\frac94$

Question ID: 20170030040

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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
$\frac{169}{4}$

Question ID: 20170030080

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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
${\left(x+5\right)}^2+3$

Question ID: 20170040030

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d) $x^2+16x+70$

a
${\left(x+8\right)}^2+6$

Question ID: 20170040040

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e) $x^2+20x+120$

a
${\left(x+10\right)}^2+20$

Question ID: 20170040050

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f) $x^2+8x+16$

a
${\left(x+4\right)}^2$

Question ID: 20170040060

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g) $x^2+12x+50$

a
${\left(x+6\right)}^2+14$

Question ID: 20170040070

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h) $x^2+18x+110$

a
${\left(x+9\right)}^2+29$

Question ID: 20170040080

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**Question 5**

Complete the square

a) $x^2+6x+8$

a
${\left(x+3\right)}^2-1$

Question ID: 20170050010

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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
${\left(x+6\right)}^2-3$

Question ID: 20170050030

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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
${\left(x+5\right)}^2-13$

Question ID: 20170050050

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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
${\left(x+1\right)}^2-2$

Question ID: 20170050070

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h) $x^2+18x-219$

a
${\left(x+9\right)}^2-300$

Question ID: 20170050080

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**Question 6**

Complete the square

a) $x^2-6x+11$

a
${\left(x-3\right)}^2+2$

Question ID: 20170060010

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b) $x^2-10x+29$

a
${\left(x-5\right)}^2+4$

Question ID: 20170060020

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c) $x^2-8x+26$

a
${\left(x-4\right)}^2+10$

Question ID: 20170060030

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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
${\left(x-11\right)}^2+17$

Question ID: 20170060050

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f) $x^2-4x+1$

a
${\left(x-2\right)}^2-3$

Question ID: 20170060060

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g) $x^2-2x-5$

a
${\left(x-1\right)}^2-4$

Question ID: 20170060070

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h) $x^2-22x+76$

a
${\left(x-11\right)}^2-45$

Question ID: 20170060080

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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__

**Question 1**

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**Question 9**

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