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

Question

A. x=6, x=-6

B. x=6

C. x=18, x=-18

D. x=-6

Answer 1

To solve the equation \( x^2 - 36 = 0 \) by factoring using the difference of squares pattern, we can rewrite it as:

\[ x^2 - 6^2 = 0 \]

This is a difference of squares, which can be factored as:

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

Setting each factor equal to zero gives us:

1. \( x - 6 = 0 \) → \( x = 6 \)
2. \( x + 6 = 0 \) → \( x = -6 \)

Thus, the solutions to the equation are \( x = 6 \) and \( x = -6 \).

The correct answer is:

A. x = 6, x = -6