What is the solution set for the equation: x² - 1 = 0?

To solve the equation x² - 1 = 0, we can factor it using the difference of squares. The difference of squares states that a² - b² can be factored into (a + b)(a - b). In this case, we have:

x² - 1 = (x - 1)(x + 1) = 0.

Setting each factor equal to zero gives us the possible solutions:

1. x - 1 = 0, which simplifies to x = 1.

2. x + 1 = 0, which simplifies to x = -1.

Thus, the solutions to the equation are x = 1 and x = -1. This solution set matches the correct answer, indicating that x can take on two values: 1 and -1. Therefore, the correct answer is that the solution set consists of the numbers 1 and -1.

The other choices do not align with the correct factorization or solutions derived from the equation set to zero. For instance, stating x = 0 would imply solving x² = 1, which does not apply here, as it overlooks the need to factorize properly. Similarly, the presence of -2 in another option is