Free Printable Completing the Square

1.

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

2.

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

3.

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

a)

4

b)

2

c)

8

d)

20

4.

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

a)

4

b)

16

c)

64

d)

-16

5.

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

a)

2

b)

4

c)

-2

d)

1

6.

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

7.

Find the value of "c" that completes the square.

x_{ }^2+8x+c

a)

-4

b)

4

c)

8

d)

16

8.

Find the value of "c" that completes the square.

x^2+28x+c

a)

28

b)

14

c)

196

d)

56

9.

Find the value of "c" that completes the square.

t^2+7t+c

a)

$\frac{7}{2}$

b)

3.5

c)

$\frac{49}{4}$

d)

$\frac{49}{2}$

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.

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

13.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

14.

What is the formula of calculate the new C-term

a)

C = $\frac{b}{2}$

b)

C = $\frac{-b}{2a}$

c)

C = $\left(\frac{b}{2}\right)^2$

d)

C = $\left(\frac{b}{4}\right)^2$

15.

When factoring $x^2-10x+25\ =\ 49$
what goes into the blank $\left(x-\ldots\right)^2=49$

a)

5

b)

10

c)

7

d)

25

Completing the Square

Total questions: 15

Worksheet time: 15mins

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