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The equation provided is \( x^2 - 25 = 0 \).

This is a quadratic equation. To solve for \( x \), let's follow these steps:

1. Start with the equation:
   \[
   x^2 - 25 = 0
   \]

2. Add 25 to both sides:
   \[
   x^2 = 25
   \]

3. Take the square root of both sides:
   \[
   x = \pm \sqrt{25}
   \]

4. Simplify the square root:
   \[
   x = \pm 5
   \]

Thus, the solutions for \( x \) are:
\[
x = 5 \quad \text{or} \quad x = -5
\]

Would you like further details or have any questions on this solution?

Here are 5 related questions to explore:
1. How would you solve a quadratic equation with a term like \( x^2 - 49 = 0 \)?
2. Can quadratic equations always be solved using square roots?
3. What are other methods to solve quadratic equations?
4. What is the significance of the plus-minus sign in the solution?
5. How do you factor a quadratic expression like \( x^2 - 25 \)?

**Tip:** For equations like \( x^2 - c = 0 \), use the difference of squares to factor the expression as \( (x - \sqrt{c})(x + \sqrt{c}) = 0 \).

Solve for all real values of x: x^2 - 25 = 0

Learn how to solve the quadratic equation x^2 - 25 = 0 by using square roots and the difference of squares. This step-by-step guide explains the solution for real values of x, suitable for students in Grades 7-9.

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