Question

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)%0D%0AResponses%0D%0A%0D%0Ax=18, x=−18%0D%0Ax equals 18 , x equals negative 18%0D%0A%0D%0Ax=−6%0D%0Ax equals negative 6%0D%0A%0D%0Ax=6%0D%0Ax equals 6%0D%0A%0D%0Ax=6, x=−6%0D%0Ax equals 6 , x equals negative 6

Answer 1

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

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

This is a difference of squares, which factors into:

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

To find the solutions, we set each factor equal to zero:

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

Thus, the correct solutions are:

\[ x = 6, \quad x = -6 \]

So the correct response from the options provided is:

\(x = 6, , x = -6\)