SOLUTION: Completing the Square: Angelique wants to have a rug that is 9 feet long and 7 feet wide in her bedroom. The rug will cover the whole floor except a border that is x feet wide. The

Question 581689: Completing the Square: Angelique wants to have a rug that is 9 feet long and 7 feet wide in her bedroom. The rug will cover the whole floor except a border that is x feet wide. The area of her room is 168 square feet. Find the width of the border, x. Round your answer to the nearest tenth of a foot.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Completing the Square: Angelique wants to have a rug that is 9 feet long and 7 feet wide in her bedroom.
The rug will cover the whole floor except a border that is x feet wide.
The area of her room is 168 square feet.
Find the width of the border, x. Round your answer to the nearest tenth of a foot.
:
From the information given we know the overall dimensions of the room is:
(2x+9) by (2x+7)
The area of the room:
(2x+9)(2x+7) = 168
FOIL
4x^2 + 14x + 18x + 63 = 168
4x^2 + 32x + 63 - 168 = 0
4x^2 + 32x - 105 = 0
Solve by completing the square, we want the coefficient of x^2 to be 1, divide equation by 4
x^2 + 8x - = 0
x^2 + 8x + ___ =
Find the value that will complete the square (8/2)^2 = 16, add to both sides
x^2 + 8x + 16 = + 16
x^2 + 8x + 16 = +
x^2 + 8x + 16 =
(x+4)^2 =
Find the square root of both side
x + 4 = +/-
x = -4 + = 2.5 ft
and
x = -4 - = -10.5
:
Obviously, x = 2.5 is the reasonable answer
:
:
See if this checks out, find the area (2x = 5)
(5+9)(5+7) = 168

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