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