Question

The product of two consecutive integers is 72. The equation x(x + 1) = 72 represents the situation, where x represents the smaller integer. Which equation can be factored and solved for the smaller integer?

x2 + x – 72 = 0
x2 + x + 72 = 0
x2 + 2x – 72 = 0
x2 + 2x + 72 = 0

Answer 1

The correct equation that can be factored and solved for the smaller integer is:

x^2 + x - 72 = 0

This equation can be factored into:

(x + 9)(x - 8) = 0

Setting each factor to 0 gives the possible values for x:

x + 9 = 0
x = -9

x - 8 = 0
x = 8

Therefore, the possible values for x are -9 and 8, but since x represents the smaller integer in this case, x = 8 is the correct solution.