Gabriel was asked to solve x2−36=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)

Question

Responses

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

x=6
x equals 6

x=6, x=−6
x equals 6 , x equals negative 6

x=−6

Answer 1

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

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

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 \(x^2 - 36 = 0\) are:

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

The correct response is:

x=6, x=−6 (x equals 6, x equals negative 6).