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.

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) (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

Use quadratic equation to solve

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=529 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8, -15. Here's your graph:

or factor as

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

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