Final answer:
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).