Question

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 start by recognizing that \( 36 \) can be expressed as \( 6^2 \). Therefore, we can rewrite the equation as:

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

This expression fits the difference of squares formula, which is given by:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In our case, \( a = x \) and \( b = 6 \). Applying the difference of squares formula, we can factor the equation as follows:

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

Next, we set each factor equal to zero to find the solutions:

1. Setting the first factor to zero:
\[
x - 6 = 0 \implies x = 6
\]

2. Setting the second factor to zero:
\[
x + 6 = 0 \implies x = -6
\]

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

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

In summary, the correct solutions are \( x = 6 \) and \( x = -6 \).