Final answer:
To solve the equation, we can break it down into two separate cases based on the absolute value. Solving each case separately gives us the solutions: x = -8, -1, and 2.
Step-by-step explanation:
To solve the equation |x² - 4x - 5| = -3x - 3, we can break it down into two separate cases based on the absolute value.
Case 1: x² - 4x - 5 = -3x - 3
Simplifying this equation gives us x² - x - 2 = 0.
We can solve this quadratic equation by factoring or using the quadratic formula to find two possible values for x: x = -1 and x = 2.
Case 2: -(x² - 4x - 5) = -3x - 3
Simplifying this equation gives us -x² + 4x + 5 = -3x - 3.
Rearranging terms gives us x² + 7x + 8 = 0.
We can solve this quadratic equation to find two more possible values for x: x = -1 and x = -8.
So the solutions to the equation are x = -8, -1, and 2.