Question

Solve the quadratic equation x^2 + x = 72 by factoring.

(A) x = 8, x = 9
(B) x = –9, x = –8
(C) x = –8, x = 9
(D) x = –9, x = 8

Answer 1

The quadratic equation x^2 + x = 72 can be factored as (x + 9)(x - 8) = 0. Setting each factor to zero, we find the solutions x = -9 and x = 8, which corresponds to option (D).

Step-by-step explanation:

To solve the quadratic equation x^2 + x = 72 by factoring, we first move all terms to the left side of the equation to set it equal to 0: x^2 + x - 72 = 0. Now we need to find two numbers that multiply to -72 and add up to 1, which are 9 and -8.

Therefore, we can factor the quadratic equation as: (x + 9)(x - 8) = 0. To find the solutions for x, we set each factor equal to zero which gives us x = -9 and x = 8.

Thus, the solutions to the equation x^2 + x = 72 by factoring are x = -9 and x = 8 which corresponds to option (D).