SOLUTION: A soccer field has an area of 135 square feet. The length is 3 feet longer than the width. What are the dimesions of the feet?

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Question 431596: A soccer field has an area of 135 square feet. The length is 3 feet longer than the width. What are the dimesions of the feet?
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
If the soccer field 135sq.ft. in area, then LXW =135. Also, we know that L equals W+3. Substituting for L we get:
(W+3)(W)=135
W2+3W=135
W2+3W-135=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-135+=+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-135=549.

Discriminant d=549 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+549+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+549+%29%29%2F2%5C1+=+10.21537451386
x%5B2%5D+=+%28-%283%29-sqrt%28+549+%29%29%2F2%5C1+=+-13.21537451386

Quadratic expression 1x%5E2%2B3x%2B-135 can be factored:
1x%5E2%2B3x%2B-135+=+1%28x-10.21537451386%29%2A%28x--13.21537451386%29
Again, the answer is: 10.21537451386, -13.21537451386. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-135+%29


(Throw out the negative value, since our soccer field isn't imaginary)