Question

Solve (x-1)²-16=0, where x is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas.

Answer 1

The equation (x-1)²-16=0 is solved by recognizing it as a difference of squares, which factors into (x-5)(x+3)=0, yielding the solutions x=5 and x=-3.

Step-by-step explanation:

To solve the equation (x-1)²-16=0, where x is a real number, we first look at the left side and recognize it as a difference of squares.

• (x - 1)² - 16 = (x - 1 - 4)(x - 1 + 4)
• (x - 5)(x + 3) = 0

By setting each factor equal to zero, we find the two possible solutions:

1. x - 5 = 0, which gives us x = 5
2. x + 3 = 0, which gives us x = -3

Therefore, the solutions to the equation are x = 5, -3.