SOLUTION: A square field has 5m added to its length and 2m added to its width.The field then had an area of 130m^2.Find the length of the side of the original field.

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Question 184114: A square field has 5m added to its length and 2m added to its width.The field then had an area of 130m^2.Find the length of the side of the original field.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let the original field's sides be x.
The new field has length (x+5) and width (x+2)
Area of a rectangle is given as A+=+L%2AW
130+=+%28x%2B5%29%28x%2B2%29
130+=+x%5E2+%2B+7x+%2B+10
0+=+x%5E2+%2B+7x+-+120
Use quadratic equation to solve
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B-120+=+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=%287%29%5E2-4%2A1%2A-120=529.

Discriminant d=529 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+529+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+529+%29%29%2F2%5C1+=+8
x%5B2%5D+=+%28-%287%29-sqrt%28+529+%29%29%2F2%5C1+=+-15

Quadratic expression 1x%5E2%2B7x%2B-120 can be factored:
1x%5E2%2B7x%2B-120+=+1%28x-8%29%2A%28x--15%29
Again, the answer is: 8, -15. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-120+%29


or factor as
0+=+%28x-8%29%28x%2B15%29
Either way, the possible original sides are 8 or -15. Since the original field cannot have a negative length side, the answer must be 8meters on each side