Gabriel was asked to solve x^2 −36=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?

Answer 1

To solve the equation \( x^2 - 36 = 0 \) using the difference of squares pattern, we can recognize that this expression can be factored as follows:

\[ x^2 - 36 = (x - 6)(x + 6) \]

Setting the factored expression equal to zero gives us:

\[ (x - 6)(x + 6) = 0 \]

This means that either \( x - 6 = 0 \) or \( x + 6 = 0 \).

Solving these equations, we find:

1. From \( x - 6 = 0 \): \[ x = 6 \]

2. From \( x + 6 = 0 \): \[ x = -6 \]

Thus, the solutions to the equation \( x^2 - 36 = 0 \) are:

\[ x = 6 \quad \text{and} \quad x = -6 \]