How do you solve the equation x² - 16 = 0?

• A. x = 4
• B. x = -4
• C. x = ±4
• D. x = 0

Answer: (C)

To solve the equation x² - 16 = 0, we start by recognizing that this is a difference of squares. The expression can be factored as follows:

x² - 16 = (x - 4)(x + 4) = 0.

This means that the equation is satisfied when either factor is zero. Setting each factor to zero gives us two equations:

1. x - 4 = 0, which simplifies to x = 4.

2. x + 4 = 0, which simplifies to x = -4.

Thus, the solutions to the equation are x = 4 and x = -4. The use of "±" is a concise way to express both solutions simultaneously, indicating that x can either be positive 4 or negative 4.

Therefore, it is accurate to conclude that the solution can be represented as x = ±4. This notation indicates both values succinctly, which is why it is the correct answer.