Solve by Completing the Square

Question

Matalea created a rectangle where the length was eight more than the width. She then determined that the area of a rectangle could be found by using the function A(x)= x²+8x where x is the width of the rectangle. If the area of the rectangle is 33 in.², what is the width of the rectangle?

Answer 1

x^2 +8x = 33

x^2 +8x +16 = 33+16

(x+4)^2 = 49

x+4 =7

x =7-4 = 3

width = 3 inches