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) Responses x=−6 x equals negative 6 x=18, x=−18 x equals 18 , x equals negative 18 x=6, x=−6 x equals 6 , x equals negative 6 x=6

Answer 1

To solve the equation \(x^2 - 36 = 0\) using factoring and the difference of squares pattern, you can factor it as follows:

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

Setting each factor equal to zero gives:

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

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

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

So the correct response is:

• \(x = 6, x = -6\)
• or equivalently, \(x\) equals \(6\), \(x\) equals negative \(6\).