Free Printable Solve quadratic Equations using completing the Square

1.

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

a)

$a^2\ -14a\ +\ 49$

b)

$a^2\ -7a\ +\ 49$

c)

$a^2\ +\ 14a\ +\ 49$

d)

$a^2\ -49$

2.

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

a)

$x^2\ +\ 3x\ +\ 15$

b)

$x^2\ +\ 9$

c)

$x^2\ -6x\ +\ 9$

d)

$x^2\ +\ 6x\ +9$

3.

$\left(2x\ +\ 1\right)^2$

a)

$4x^2\ +1$

b)

$2x^2\ +\ 2x\ +\ 1$

c)

$4x^2\ +\ 4x\ +1$

d)

$4x^2\ +\ 2x\ +\ 1$

4.

$\sqrt{63}$

a)

$9\sqrt{7}$

b)

$6\sqrt{2}$

c)

$7\sqrt{6}$

d)

$3\sqrt{7}$

5.

$\sqrt{96}$

a)

$16\sqrt{6}$

b)

$2\sqrt{6}$

c)

$4\sqrt{6}$

d)

$\sqrt{2}$

6.

$\sqrt{50}$

a)

$5\sqrt{2}$

b)

$\sqrt{5}$

c)

$2\sqrt{5}$

d)

$25\sqrt{2}$

7.

$\sqrt{243}$

a)

$3\sqrt{3}$

b)

$9\sqrt{3}$

c)

$81\sqrt{3}$

d)

$3\sqrt{81}$

8.

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

9.

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

10.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

11.

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

a)

4

b)

2

c)

8

d)

20

12.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

13.

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

14.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

15.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

16.

Solve for x by taking the Square Root:

(x+6)²= 49

a)

x = 7 and 12

b)

x = ±7

c)

x = 1 and -13

d)

x = 43 and -55

17.

Solve the equation using square roots:

x² = 121

a)

x = 60.5

b)

x = ± 11

c)

x = ± 12

d)

x= 11

18.

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

19.

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

20.

Solve by completing the square.
x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

Solve quadratic Equations using completing the Square

Total questions: 20

Worksheet time: 3hrs 43mins

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