The area of a rectangle is given by A (x) = x2 + 5x with x being the height and x + 5 being the base. If the area is 14, what is the only viable solution for the height? Why are there not two solutions?

See below.

Step-by-step explanation:

A (x) = x^2 + 5x

A (x) = x^2 + 5x = 14

x^2 + 5x - 14 = 0

(x + 7) (x - 2) = 0

x + 7 = 0 or x - 2 = 7

x = - 7 or x = 2

x is the height of a rectangle.

The only viable solution is x = 2 because the height of a rectangle cannot be a negative number such as - 7.