SOLUTION: An Architect is designing a rectangular meeting room so that the length is 8 feet greater than 4 times the width. The are of the room needs to be 3200.

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Question 173809: An Architect is designing a rectangular meeting room so that the length is 8 feet greater than 4 times the width. The are of the room needs to be 3200.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
A=LW
but, L=8%2B4W
Then, 3200=%288%2B4W%29%28W%29
3200=8W%2B4W%5E2
4W%5E2%2B8W-3200=0, divide the whole eqn by 4:
W%5E2%2B2W-800=0
Let W=x, solve by Quadratic:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-800+=+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=%282%29%5E2-4%2A1%2A-800=3204.

Discriminant d=3204 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+3204+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+3204+%29%29%2F2%5C1+=+27.3019433961698
x%5B2%5D+=+%28-%282%29-sqrt%28+3204+%29%29%2F2%5C1+=+-29.3019433961698

Quadratic expression 1x%5E2%2B2x%2B-800 can be factored:
1x%5E2%2B2x%2B-800+=+1%28x-27.3019433961698%29%2A%28x--29.3019433961698%29
Again, the answer is: 27.3019433961698, -29.3019433961698. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-800+%29

.
highlight%28W=27.3ft%29
L=8%2B4%2827.3%29=highlight%28117.2ft%29
check;
3200=27.3%2A117.2
3200ft%5E2=3199.56ft%5E2 close enough
Thank you,
Jojo