To solve the equation \( x^2 - 36 = 0 \) using factoring, we can recognize that it is a difference of squares. The difference of squares can be factored as follows:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we have:
\[ x^2 - 6^2 = (x - 6)(x + 6) \]
Therefore, we can write the equation as:
\[ (x - 6)(x + 6) = 0 \]
Now, we set each factor equal to zero:
- \( x - 6 = 0 \) → \( x = 6 \)
- \( x + 6 = 0 \) → \( x = -6 \)
Thus, the solutions to the equation \( x^2 - 36 = 0 \) are \( x = 6 \) and \( x = -6 \).
The correct answer that includes both solutions is:
C: x = 6, x = -6.