Final answer:
The student needs to solve a quadratic equation by factoring, which involves finding two numbers that add to 17 and multiply to 72, leading to the solutions x = -8 and x = -9 after factoring the equation and setting each factor to zero.
Step-by-step explanation:
The student is asking to solve a quadratic equation by factoring.
The equation presented is in the form of x^2 + 17x = -72, which can be rearranged to x^2 + 17x + 72 = 0 in order to set it equal to zero, which is necessary for factoring.
To solve the equation, one must find two numbers that both add up to 17 and multiply to give 72.
These numbers are 8 and 9, thus the equation factors to (x + 8)(x + 9) = 0.
The solutions for x are where each factor equals zero, meaning x = -8 and x = -9.
It's important to check both solutions to ensure that they make the original equation true.