SOLUTION: A corner lot has dimensions 25 by 40 yards. The city plans to take a strip of uniform width along the two sides bordering the streets to widen these roads. How wide should the stri

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Question 911166: A corner lot has dimensions 25 by 40 yards. The city plans to take a strip of uniform width along the two sides bordering the streets to widen these roads. How wide should the strip be if the remainder of the lot is to have an area of 844 square yards? (Round your answer to two decimal places.)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
25%2A40+-+844+=+156yd%5E2
(corner lot)
25x + (40-x)x = 156
x^2 -65x + 156 = 0
x = 2.50yd
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-65x%2B156+=+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=%28-65%29%5E2-4%2A1%2A156=3601.

Discriminant d=3601 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--65%2B-sqrt%28+3601+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-65%29%2Bsqrt%28+3601+%29%29%2F2%5C1+=+62.504166377355
x%5B2%5D+=+%28-%28-65%29-sqrt%28+3601+%29%29%2F2%5C1+=+2.49583362264501

Quadratic expression 1x%5E2%2B-65x%2B156 can be factored:
1x%5E2%2B-65x%2B156+=+1%28x-62.504166377355%29%2A%28x-2.49583362264501%29
Again, the answer is: 62.504166377355, 2.49583362264501. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-65%2Ax%2B156+%29