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Worksheets

Solve by Completing the Square

Total questions: 15

Worksheet time: 15mins

Name
Class
Date
1.

Solve for x.

(x - 7)2 + 4 = 40

a)

x = -1, -13

b)

x = 1, 7

c)

x = -1, -7

d)

x = 1, 13

e)

x = -7, -13

2.

Solve by completing the square:
v2 + 6v − 59 = 0

a)

{-5 + 5√2, -5 - 5√2}

b)

{5 + 5√2, 5 - 5√2}

c)

{-3 + 2√17, -3 - 2√17}

d)

{3 + 2√17, 3 - 2√17}

3.

Solve the following equation by completing the square:
n2 = 18n + 40

a)

{11, -11}

b)

{16, 2}

c)

{20, -2}

d)

{10, -4}

4.

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

5.

To solve by completing the square, what needs to be moved in this equation?
x2 = 9 - 4x

a)

the -4x

b)

the 9

c)

the x2

6.

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

a)

4

b)

2

c)

8

d)

20

7.

Solve by completing the square:

n2 - 2n - 3 = 0

a)

n = 3 and -1

b)

n = 4 and -4

c)

n = 5 and -3

d)

n = 8 and -7

8.

Solve by completing the square:

x2 + 10x = -9

a)

x = 1 and -12

b)

x = -1 and -9

c)

x = 1 and -9

d)

x = 1 and -1

9.

Solve by completing the square:

k2 − 12k + 20 = 0

a)

k = 10 and 2

b)

k = -6 and -6

c)

k = 22 and -10

d)

k = -2 and 6

10.

Complete the Square
x2 + 6x + 5

a)

(x + 3)2 - 4

b)

(x + 6)2 - 4

c)

(x + 3x)2 - 4

d)

(x + 3)2 + 9

11.

Complete the Square
x2 + 10x + ____

a)

x2 + 10x - 100

b)

x2 + 10x + 100

c)

x2 + 10x - 25

d)

x2 + 10x + 25

12.

Complete the square.
x2 + 6x + ____

a)

x2 + 6x + 9

b)

x2 + 6x - 36

c)

x2 + 6x + 36

d)

x2 + 6x - 9

13.

Complete the Square
x2 - 12x

a)

(x + 6)2 + 12

b)

(x - 6)2 - 24

c)

(x - 6)2 - 12

d)

(x - 6)2 - 36

14.

Complete the Square
x2 + 6x + 20

a)

(x + 3x)2 + 11

b)

(x + 3)2 + 11

c)

(x + 6)2 + 11

d)

(x + 3)2 + 29

15.

What should be added to both sides of the following equation to complete the square?
x2 + 12x = 5

a)

12

b)

6

c)

36

d)

5