Solve the Equation by Completing the Square Worksheet

**Page 1**

1.

Solve $x$^{2} + 10$x$ = 39 by completing the square.

a. | 1 and - 39 | ||

b. | 10 and 39 | ||

c. | - 13 and - 3 | ||

d. | - 13 and 3 |

[Original equation.]

[Add (

(

[Writing left side as perfect square.]

(

[Finding square roots on each side.]

[Subtract 5 from each side.]

[Simplify.]

The solutions of the equation

Correct answer : (4)

2.

Solve $x$^{2} - 6$x$ = 27 by completing the square.

a. | 11 and - 3 | ||

b. | - 9 and - 3 | ||

c. | 9 and - 7 | ||

d. | 9 and - 3 |

[Original equation.]

[Add (-

(

[Write left side as perfect square and simplify.]

[Evaluate square roots on both sides.]

[Add 3 to each side.]

[Simplify.]

The solutions of the equation

Correct answer : (4)

3.

The area of the right triangle shown is 96 square cm. Find the value of $x$.

a. | 10 | ||

b. | 14 | ||

c. | 12 | ||

d. | 17 |

96 =

[Substitute A = 96, height =

96 × 2 =

[Multiply each side by 2.]

192 =

[Simplify.]

192 =

[Use distributive property.]

192 + 2

[To make RHS a perfect square, add (

196 = (

[Write right side as a perfect square.]

± 14 = (

[Find square roots on each side.]

[Subtract 2 from each side.]

[Since

Correct answer : (3)

4.

The area of the parallelogram is 16 cm^{2}. What is its length?

a. | 8 cm | ||

b. | 7 cm | ||

c. | 5 cm | ||

d. | 6 cm |

16 =

[Original equation.]

16 =

[Use distributive property to simplify.]

16 + 3

[Add (

25 = (

[Write right side as a perfect square and simplify.]

± 5 = (

[Evaluate square roots on both sides.]

[Subtract 3 from each side.]

[Simplify.]

Height of the parallelogram is

[Since height cannot be a negative value.]

Length =

[Simplify.]

Correct answer : (1)

5.

What term should be added to the expression $x$^{2} - 4$x$, to create a perfect square trinomial?

a. | - 16 | ||

b. | - 4 | ||

c. | 16 | ||

d. | 4 |

[Original expression.]

Add to the expression

The coefficient

4 should be added to the expression

Correct answer : (4)

6.

George wants to fence a rectangular plot. The area of the plot is 20900 ft^{2}. Find the dimensions of the plot if the length is 80 feet more than the width.

a. | 200 ft by 120 ft | ||

b. | 190 ft by 110 ft | ||

c. | 150 ft by 70 ft | ||

d. | 250 ft by 170 ft |

20900 =

[Write an equation.]

20900 =

[Use distributive property.]

20900 + 40

[Add (

22500 = (

[Write the right side expression as a perfect square.]

± 150 = (

[Apply square root on each side.]

[Subtract 40 from each side.]

[Discard the negative value of

So, the plot will be 190 ft long and 110 ft wide.

Correct answer : (2)

7.

What term should be added to the expression, $x$^{2} - 12$x$ to create a perfect square trinomial?

a. | - 36 | ||

b. | 6 | ||

c. | 36 | ||

d. | 1 |

[Original expression.]

Add to the expression

The coefficient of

36 should be added to the expression

Correct answer : (3)

8.

What term should be added to the expression, $x$^{2} + 4$x$ to create a perfect square trinomial?

a. | 5 | ||

b. | 4 | ||

c. | - 4 | ||

d. | 2 |

[Original expression.]

Add to the expression

The coefficient of

4 should be added to the expression

Correct answer : (2)

9.

Charles's apartment complex has a rectangular skating floor. The floor is $x$ ft long and ($x$ + 6) ft wide. What are the dimensions of the skating floor, if its area is 616 ft^{2}?

a. | 22 ft by 23 ft | ||

b. | 22 ft by 31 ft | ||

c. | 24 ft by 28 ft | ||

d. | 22 ft by 28 ft |

616 =

[Original equation.]

616 =

[Use distributive property to simplify.]

616 + 3

[Add (

625 = (

[Write right side as a perfect square and simplify.]

± 25 = (

[Evaluate square roots on both sides.]

[Subtract 3 from each side.]

[Simplify.]

The skating floor is

[Since

Correct answer : (4)

10.

A rectangular painting is $a$ inches wide and $a$ + 8 inches long. What are the dimensions of the painting , if the area of the painting is 128 inches^{2}?

a. | 10 inches by 18 inches | ||

b. | 16 inches by 8 inches | ||

c. | 9 inches by 17 inches | ||

d. | 11 inches by 19 inches |

The area of the rectangular painting = (

128 = (

[Original equation.]

128 =

[Use distributive property.]

128 + 4

[Add (

144 = (

[Write the right side of the equation as a perfect square and simplify.]

± 12 = (

[Evaluate square roots on both the sides.]

± 12 - 4 =

[Subtract 4 from each side.]

[Simplify.]

Width of the rectangular painting is

[Since the dimensions cannot be negative.]

Length of the rectangular painting is (

[Replace

The dimensions of the rectangular painting are 16 inches by 8 inches.

Correct answer : (2)