Gabriel was asked to solve x2−36=0

Question

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

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

This is a difference of squares, which can be factored as:

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

Now, we set each factor equal to zero:

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.