Free Printable Completing the square

1.

Complete the square for

x² - 12x + ____

a)

144

b)

36

c)

- 36

d)

24

2.

Complete the square.

x² + 6x + ____

a)

9

b)

12

c)

36

d)

- 9

3.

Complete the Square

x² - 10x + ____

a)

x² + 10x - 100

b)

x² - 10x + 100

c)

x² + 10x - 25

d)

x² - 10x + 25

4.

Find the missing value "c" to create a perfect square trinomial:
x² – 8x + ___

a)

-4

b)

16

c)

4

d)

8

5.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

6.

Find the value of c to make it a perfect square trinomial.

x²+5x+c

a)

10

b)

25

c)

25/2

d)

25/4

7.

Complete the Square and solve the equation.
a² - 2a - 35 = 0

a)

1 ± √ 6

b)

-7, 7

c)

-5, 7

d)

35, 37

8.

Complete the Square and solve the equation.
m² + 12m + 19 = 0

a)

- 6 ± √ - 19

b)

6 ± √ 19

c)

- 23, - 11

d)

- 6 ± √ 17

9.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

10.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

11.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

12.

Complete the square.

x² - 14x + ____

a)

- 196

b)

49

c)

- 49

d)

28

13.

Complete the Square

x² - 10x + ____

a)

x² + 10x - 100

b)

x² - 10x + 100

c)

x² + 10x - 25

d)

x² - 10x + 25

14.

$x^2-4x-32=0$

a)

$\left\{6,-4\right\}$

b)

$\left\{11,1\right\}$

c)

$\left\{8,-4\right\}$

d)

$\left\{10,-2\right\}$

15.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

16.

Find the last term:

x^2+22x+c

a)

22

b)

11

c)

121

d)

44

17.

Find the last term:

x^2-8x+c

a)

8

b)

4

c)

-16

d)

16

18.

Find the last term:

x^2-16x+c

a)

8

b)

64

c)

-16

d)

16

19.

Find the last term:

x^2+34x+c

a)

289

b)

17

c)

34

d)

-34

20.

Find the last term:

x^2+30x+c

a)

30

b)

15

c)

225

d)

-15

21.

Find the last term:

x^2+4x+c

a)

4

b)

2

c)

-2

d)

-4

22.

Find the last term:

x^2-6x+c

a)

-9

b)

9

c)

6

d)

-6

23.

Find the last term:

x^2+10x+c

a)

5

b)

2

c)

20

d)

25

24.

Find the last term:

x^2+12x+c

a)

36

b)

21

c)

16

d)

25

25.

Find the last term:

x^2+42x+c

a)

-9

b)

21

c)

441

d)

1764

26.

Find the last term:

x^2-2x+c

a)

-2

b)

1

c)

-1

d)

2

27.

Find the last term:

x^2-28x+c

a)

14

b)

200

c)

169

d)

196

28.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

29.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

30.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

31.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

32.

Complete the Square

x² + 6x - 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

33.

What do you need to add to complete the square?x² + 6x = 20

a)

9

b)

100

c)

36

d)

12

34.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

35.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

36.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

37.

Complete the Square
x² + 10x + ____

a)

x² + 10x - 100

b)

x² + 10x + 100

c)

x² + 10x - 25

d)

x² + 10x + 25

38.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

39.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

40.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

41.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

42.

Complete the square for

x² - 12x + ____

a)

144

b)

36

c)

- 36

d)

24

43.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

44.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

45.

What value of c would make this a perfect square trinomial?
x²- 12x + c

a)

36

b)

24

c)

144

d)

-36

46.

Find the missing value "c" to create a perfect square trinomial:
x² + 26x + ___

a)

13

b)

136

c)

169

d)

26

47.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

48.

Complete the square for

x² + 12x + ____

(find the missing number in the blank)

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

49.

Complete the square.

x² - 14x + ____

a)

- 196

b)

49

c)

- 49

d)

28

50.

Complete the square.

x² + 6x + ____

a)

9

b)

12

c)

36

d)

- 9

51.

Complete the Square

x² - 10x + ____

a)

x² + 10x - 100

b)

x² - 10x + 100

c)

x² + 10x - 25

d)

x² - 10x + 25

52.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

53.

Given the perfect square trinomial, identify the equivalent expression

x²+14x+49

a)

(x+14)²

b)

(x+49)²

c)

(x-7)²

d)

(x+7)²

54.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

55.

Complete the square and write the equation in Vertex Form:
f(x) = x² + 16x + 64

a)

f(x) = (x - 8)²

b)

f(x) = (x+16)²

c)

f(x) = x²+ 8

d)

f(x) = (x+8)²

56.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

57.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

58.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

59.

$x^2+6x-4=0$

Complete the Square. Do not solve!

a)

$\left(x+3\right)^2=13$

b)

$\left(x-3\right)^2=-5$

c)

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

d)

$\left(x-3\right)^2=13$

60.

$x^2-24x-10=0$ Complete the Square. Do not solve!

a)

$\left(x-12\right)^2=134$

b)

$\left(x+12\right)^2=154$

c)

$\left(x-12\right)^2=154$

d)

$\left(x+12\right)^2=134$

61.

What is your favorite weather?

4 lines

62.

Choose the number that goes in the blank to create a perfect square trinomial.

$x^2+12x+$ _____

a)

36

b)

144

c)

6

d)

24

63.

Choose the number that goes in the blank to create a perfect square trinomial.

$x^2+20x+$ _____

a)

50

b)

40

c)

100

d)

20

64.

Choose the number that goes in the blank to create a perfect square trinomial.

$x^2-24x+$ _____

a)

12

b)

144

c)

100

d)

-144

65.

Factor the following perfect square trinomial.

$x^2-14x+49$

a)

$\left(x+7\right)^2$

b)

$\left(x-7\right)^2$

c)

$\left(x+7\right)\left(x-7\right)$

d)

$\left(x-14\right)^2$

66.

Factor the following perfect square trinomial.

$x^2+22x+121$

a)

$\left(x+22\right)^2$

b)

$\left(x+12\right)^2$

c)

$\left(x+11\right)^2$

d)

$\left(x-11\right)^2$

67.

Factor the following perfect square trinomial.

$x^2+16x+64$

a)

$\left(x+16\right)^2$

b)

$\left(x+6\right)^2$

c)

$\left(x-8\right)^2$

d)

$\left(x+8\right)^2$

Completing the square

Total questions: 67

Worksheet time: 3hrs 25mins

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