Question

Solve the following quadratic by factoring x² + x - 42 = 0 (List the answers separated by a comma. For example, if you found solutions x=1 and x=2, you would enter 1,2)

Answer 1

The quadratic equation x² + x - 42 = 0 is factored to (x + 7)(x - 6) = 0. The solutions for x are found by setting each factor to zero, resulting in x = -7 and x = 6.

Step-by-step explanation:

To solve the quadratic equation x² + x - 42 = 0 by factoring, we need to find two numbers that multiply to -42 and add to 1. The numbers that fit this requirement are +7 and -6 because (7)(-6) = -42 and 7 + (-6) = 1. The factored form of the equation is (x + 7)(x - 6) = 0.

To find the solutions for x, we set each factor equal to zero:

• x + 7 = 0 → x = -7
• x - 6 = 0 → x = 6

Therefore, the solutions to the equation x² + x - 42 = 0 are x = -7, 6.