To solve the equation \( x^2 - 36 = 0 \) by factoring using the difference of squares pattern, we recognize that \( 36 \) is a perfect square:
The equation can be factored as follows:
\[ x^2 - 36 = (x - 6)(x + 6) = 0 \]
Setting each factor to zero gives us the solutions:
\[ x - 6 = 0 \quad \Rightarrow \quad x = 6 \] \[ x + 6 = 0 \quad \Rightarrow \quad x = -6 \]
Thus, the correct solutions are:
x = 6, x = -6 or x equals 6, x equals negative 6.
So, the correct response from the options provided would be:
x=6, x=−6 or x equals 6, x equals negative 6.