SOLUTION: The width of a rectangle is 18 ft less than the length. The area is 10 ft square. What is the length and width

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Question 933086: The width of a rectangle is 18 ft less than the length. The area is 10 ft square. What is the length and width
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
L = W + 18
W*L = 10
-------
W*(W+18) = 10
W^2 + 18W - 10 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B18x%2B-10+=+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=%2818%29%5E2-4%2A1%2A-10=364.

Discriminant d=364 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+364+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+364+%29%29%2F2%5C1+=+0.539392014169456
x%5B2%5D+=+%28-%2818%29-sqrt%28+364+%29%29%2F2%5C1+=+-18.5393920141695

Quadratic expression 1x%5E2%2B18x%2B-10 can be factored:
1x%5E2%2B18x%2B-10+=+%28x-0.539392014169456%29%2A%28x--18.5393920141695%29
Again, the answer is: 0.539392014169456, -18.5393920141695. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B18%2Ax%2B-10+%29

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W = 0.539392014169456 ft
L = 18.539392014169456 ft