Solving a Quadratic Equation by Completing the Square Worksheet

**Page 1**

1.

What term should be added to the expression, $x$^{2} - 6$x$, to make it a perfect square trinomial?

a. | - 9 | ||

b. | 36 | ||

c. | 9 | ||

d. | None of the above |

[Original expression.]

To complete the square of the expression

The coefficient

9 should be added to the expression,

Correct answer : (3)

2.

Josh wants to mark a rectangular plot of area 20900 ft^{2} for planting orange trees. What would be the dimensions of the plot, if he wants the length to be 80 feet more than the width?

a. | 100 ft by 200 ft | ||

b. | 150 ft by 140 ft | ||

c. | 110 ft by 190 ft | ||

d. | None of the above |

20900 =

[Write an equation.]

20900 =

[Use distributive property.]

20900 + 40

[To make the RHS a perfect square, 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

The plot will be 190 ft long and 110 ft wide.

Correct answer : (3)

3.

What term should be added to the expression, $x$^{2} - 18$x$, to create a perfect square trinomial?

a. | 81 | ||

b. | 18 | ||

c. | -81 | ||

d. | None of the above |

[Original expression.]

To complete the square of the expression

The coefficient of

81 should be added to the expression

Correct answer : (1)

4.

What term should be added to the expression, $x$^{2} + 18$x$, to create a perfect square trinomial?

a. | - 81 | ||

b. | 81 | ||

c. | 18 | ||

d. | None of the above |

[Original expression.]

To complete the square of the expression

The coefficient of

81 should be added to the expression

Correct answer : (2)

5.

Solve $x$^{2} + 4$x$ = 21 by completing the square.

a. | -7 and 3 | ||

b. | -7 and -3 | ||

c. | 1 and -21 | ||

d. | None of the above |

[Original equation.]

[Add (

(

[Writing left side as perfect square.]

(

[Finding square roots on each side.]

[Subtract 2 from each side.]

[Simplify.]

The solutions of the equation

Correct answer : (1)

6.

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

a. | 11 and -3 | ||

b. | -9 and -3 | ||

c. | 9 and -3 | ||

d. | 9 and -7 |

[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 : (3)

7.

The area of the right triangle is 70 square cm. What is the value of $x$?

a. | 10 | ||

b. | 8 | ||

c. | 15 | ||

d. | 12 |

70 =

[Substitute 70 for A,

70 x 2 =

[Multiply each side by 2.]

140 =

[Simplify.]

140 =

[Use distributive property.]

140 + 2

[To make RHS a perfect square, add (4/2)

144 = (

[Write right side as a perfect square.]

± 12 = (

[Find square roots on each side.]

[Subtract 2 from each side.]

[Since

Correct answer : (1)

8.

The area of the parallelogram 40 cm^{2}. What is its length?

a. | 7 cm | ||

b. | 9 cm | ||

c. | 10 cm | ||

d. | 8 cm |

40 =

[Original equation.]

40 =

[Use distributive property to simplify.]

40 + 3

[Add (

49 = (

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

± 7 = (

[Evaluate square roots on both sides.]

[Subtract 3 from each side.]

[Simplify.]

Height of the parallelogram =

[Since height cannot be a negative value.]

Length =

[Simplify.]

Correct answer : (3)

9.

Mr. Jim is planning to have a garden of 169 square feet. What are the dimensions of the garden, if he wants it in the form of a square?

a. | 5 feet by 5 feet | ||

b. | 13 feet by 13 feet | ||

c. | 8 feet by 8 feet | ||

d. | 20 feet by 20 feet |

The area of a square = (side)

[Original equation.]

[Find square roots on each side.]

The dimensions of the garden would be 13 feet by 13 feet.

[Dimension cannot be a negative value.]

Correct answer : (2)

10.

Joe's apartment complex has a rectangular skating floor. The floor is $x$ ft long and ($x$ + 10) ft wide. What are the dimensions of the skating floor, if its area is 600 ft^{2}?

a. | 22 ft by 30 ft | ||

b. | 20 ft by 25 ft | ||

c. | 20 ft by 30 ft | ||

d. | 20 ft by 33 ft |

600 =

[Original equation.]

600 =

[Use distributive property to simplify.]

600 + 5

[Add (

625 = (

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

±25 = (

[Evaluate square roots on both sides.]

[Subtract 5 from each side.]

[Simplify.]

The skating floor is

[Since

Correct answer : (3)