To solve the equation \( x^2 - 529 = 0 \) by exacting the square root, follow these steps:

1. **Isolate the quadratic term** \( x^2 \) by moving 529 to the other side of the equation:
   \[
   x^2 = 529
   \]

2. **Take the square root of both sides** to solve for \( x \):
   \[
   x = \pm \sqrt{529}
   \]

3. **Determine the square root of 529**:
   \[
   \sqrt{529} = 23
   \]

So, the exact solutions are:
\[
x = \pm 23
\]
This means \( x = 23 \) or \( x = -23 \).

Would you like more details or have any questions?

Here are some related questions:
1. How do you solve equations by isolating the variable?
2. What happens when the equation involves \( x^2 \) on both sides?
3. How do you handle equations with negative square roots?
4. What are the steps for solving \( x^2 + 529 = 0 \)?
5. How can you verify the solutions to \( x^2 - 529 = 0 \)?

**Tip:** When you extract the square root of both sides, always remember to include the positive and negative roots unless the context specifies otherwise.

Learn how to solve the equation x^2 - 529 = 0 step-by-step. Understand the process of isolating the quadratic term and taking the square root to find the exact solutions. Suitable for students in Grades 7-9 studying quadratic equations and square roots.

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