SOLUTION: The area of a sqaure is numerically 96 more than the perimeter. Find the length of the side.

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Question 289096: The area of a sqaure is numerically 96 more than the perimeter. Find the length of the side.
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Equation: X%5E2+=+4X+%2B+96
Set one side to 0
X%5E2+-+4X+-+96+=+0
Use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-96+=+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=%28-4%29%5E2-4%2A1%2A-96=400.

Discriminant d=400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+400+%29%29%2F2%5C1+=+12
x%5B2%5D+=+%28-%28-4%29-sqrt%28+400+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B-4x%2B-96 can be factored:
1x%5E2%2B-4x%2B-96+=+1%28x-12%29%2A%28x--8%29
Again, the answer is: 12, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-96+%29


Using the quadratic equation gave us two answers: -8 & 12
Since you can not have a negative length, 12 is the length of 1 side