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=6
x equals 6

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

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

x=−6

Answer 1

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

\[ x^2 - 36 = (x - 6)(x + 6) = 0 \]

Setting each factor equal to zero gives us:

1. \( x - 6 = 0 \) which leads to \( x = 6 \)
2. \( x + 6 = 0 \) which leads to \( x = -6 \)

Thus, the correct solutions are:

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

The appropriate response is:

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