The equation \( x^2 - 36 = 0 \) can be factored using the difference of squares pattern. The difference of squares states that \( a^2 - b^2 = (a - b)(a + b) \).
In this case, we can rewrite \( x^2 - 36 \) as:
\[ x^2 - 6^2 = (x - 6)(x + 6) \]
Setting this equal to zero gives us:
\[ (x - 6)(x + 6) = 0 \]
This means that either \( x - 6 = 0 \) or \( x + 6 = 0 \). Solving these equations:
- \( x - 6 = 0 \) leads to \( x = 6 \)
- \( x + 6 = 0 \) leads to \( x = -6 \)
Thus, the solutions to the equation \( x^2 - 36 = 0 \) are \( x = 6 \) and \( x = -6 \).
The correct answer is B) x = 6, x = -6.