Gabriel was asked to solve x^2-36=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?

Answer 1

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

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

Now, we set the factored equation equal to zero:

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

Using the zero product property, we can set each factor equal to zero:

1. \( x - 6 = 0 \)

   Solving this gives: \[ x = 6 \]

2. \( x + 6 = 0 \)

   Solving this gives: \[ x = -6 \]

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

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