Question

Gabriel was asked to solve x^2−36=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses

x=6
x equals 6

x=18, x=−18
x equals 18 , x equals negative 18

x=−6
x equals negative 6

x=6, x=−6

Answer 1

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

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

This can be factored using the difference of squares formula, \( a^2 - b^2 = (a - b)(a + b) \):

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

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:

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

So the correct response is:

**x=6, x=−6** (or "x equals 6, x equals negative 6")