To solve the equation \( x^2 = 81 \), we need to find the values of \( x \) that satisfy this equation.

### Solution:

1. **Start with the equation:**
   \[
   x^2 = 81
   \]

2. **Take the square root of both sides:**
   \[
   x = \pm \sqrt{81}
   \]

3. **Simplify the square root:**
   \[
   \sqrt{81} = 9
   \]

4. **Include both positive and negative solutions:**
   \[
   x = 9 \quad \text{or} \quad x = -9
   \]

### 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 would you solve \( x^2 = 100 \)?
2. What are the solutions to \( x^2 = 64 \)?
3. Can you find the roots of \( x^2 = 49 \)?
4. How do you solve \( x^2 = 25 \)?
5. What are the solutions to \( x^2 = 144 \)?
6. How would you solve \( x^2 = 36 \)?
7. Can you find the roots of \( x^2 = 121 \)?
8. What is the solution to \( x^2 = 16 \)?

### Tip:
When solving quadratic equations of the form \( x^2 = a \), always remember to consider both the positive and negative square roots of \( a \).

Learn how to solve the equation x^2 = 81 with a detailed step-by-step solution. This problem involves finding the square roots of 81, including both positive and negative solutions. Suitable for students in Grades 7-9.

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