A photograph has a length that is 3 inches longer than its width, x. So its area is given by the expression x (x+3) square inches. If the area of the photograph is 70 square inches, what is the length of the photograph?

The width is 10 inches.

x (x + 3) = 70

x² + 3x = 70

Subtract 70 from both sides.

x² + 3x - 70 = 0

Factor the trinomial

(x - 7) (x + 10) = 0

Set each equal to zero.

x = - 7, - 10

Distance can't be negative so x = 7 is the right one. Now we plug in for the length (x + 3)

x + 3

7 + 3

10