solving quadratic equations by factoring  ×²=81

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:
1. How do you solve \( x^2 - 100 = 0 \) by factoring?
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3. Can you find the roots of \( x^2 - 49 = 0 \) by factoring?
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7. Can you find the roots of \( x^2 - 121 = 0 \) using factoring?
8. What is the solution to \( x^2 - 16 = 0 \) by factoring?

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

Learn how to solve the quadratic equation x^2 = 81 by factoring with a detailed step-by-step solution. This problem involves recognizing a difference of squares and applying the factoring method. Suitable for students in Grades 7-9.

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