Suppose a rectangular field used to play soccer has an area of 7,800 square yards. Is the length is 70 yards longer than the width, what are the dimensions of the field?

Area of a rectangle is length times width. Let x = the width of the soccer field. That means the length of the field is x + 70.

Now take the formula for area to get A = x(x + 70)

We know area is 7,800 therefore,
7,800 = x(x + 60)
7,800 = x^2 + 70x
0 = x^2 + 70x - 7800

Factoring gives us
0 = (x + 130)(x - 60)
x = -130 or x = 60

Since we are talking about a length, x = -130 makes no sense, so the dimensions of the field are 60 by 130.