To solve the quadratic equation $x^2 = 81$ by factoring, we need to rewrite the equation in a form that can be factored. Here are the steps:

1. Rewrite the equation so one side is zero: $x^2 - 81 = 0$

2. Recognize that this is a difference of squares: $x^2 - 81 = (x + 9)(x - 9)$

3. Set each factor equal to zero: $x + 9 = 0 \quad \text{or} \quad x - 9 = 0$

4. Solve each equation: $x + 9 = 0 \implies x = -9$ $x - 9 = 0 \implies x = 9$

Final Answer:

$x = 9 \quad \text{or} \quad x = -9$

Would you like more details or have any questions about this solution?

Related Questions:

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Tip:

When factoring a quadratic equation, always check if it can be expressed as a difference of squares, which follows the pattern $a^2 - b^2 = (a + b)(a - b)$.