SOLUTION: A rectangular stained glass window is 2 feet by 4 feet. A clear glass border is constructed around the stained glass window. The width of the border is equal and was made out of 7

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Question 954524: A rectangular stained glass window is 2 feet by 4 feet. A clear glass border is constructed around the stained glass window. The width of the border is equal and was made out of 7 square feet of clear glass. What is the width of the border?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Area of window=2ft*4ft=8 sq ft
Area of window + border=8 sq ft+7 sq ft=15 sq ft
x=width added to width and length
border width=(1/2)x
%282ft%2Bx%29%284ft%2Bx%29=15ft%5E2
8%2B6x%2Bx%5E2=15ft%5E2
x%5E2%2B6x-7=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A-7=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+1
x%5B2%5D+=+%28-%286%29-sqrt%28+64+%29%29%2F2%5C1+=+-7

Quadratic expression 1x%5E2%2B6x%2B-7 can be factored:
1x%5E2%2B6x%2B-7+=+1%28x-1%29%2A%28x--7%29
Again, the answer is: 1, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-7+%29

ANSWER:Border=(1/2)x=(1/2)1ft=6 inches. .The width of the border is 6 inches.