SOLUTION: If two opposite sides of a square are increased by 9 meters and the other sides are decreased by 6 meters, the area of the rectangle that is formed is 78 square meters. Find the a

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Question 103385: If two opposite sides of a square are increased by 9 meters and the other sides are decreased by 6 meters, the area of the rectangle that is formed is 78 square meters. Find the area of the original square.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
let x=original sides of the square.
A=L*W
(x+9)(x-6)=78
x^2+3x-54=78
x^2+3x-132=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-132+=+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=%283%29%5E2-4%2A1%2A-132=537.

Discriminant d=537 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+537+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+537+%29%29%2F2%5C1+=+10.0866302262565
x%5B2%5D+=+%28-%283%29-sqrt%28+537+%29%29%2F2%5C1+=+-13.0866302262565

Quadratic expression 1x%5E2%2B3x%2B-132 can be factored:
1x%5E2%2B3x%2B-132+=+%28x-10.0866302262565%29%2A%28x--13.0866302262565%29
Again, the answer is: 10.0866302262565, -13.0866302262565. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-132+%29

The area of the original square=(10.0866...)= 101.74 sq meters
Ed