To solve the equation \( 25 = 2r^2 \) for \( r \):

1. **Isolate \( r^2 \)**:
   \[
   r^2 = \frac{25}{2}
   \]
   \[
   r^2 = 12.5
   \]

2. **Take the square root of both sides**:
   \[
   r = \pm \sqrt{12.5}
   \]

3. Simplify the square root (optional):
   \[
   r = \pm \sqrt{12.5} \approx \pm 3.54
   \]

So, the solutions are \( r \approx 3.54 \) and \( r \approx -3.54 \).

Would you like more details or have any questions? 

Here are 5 related questions to explore:

1. How do you solve \( 16 = 2r^2 \) for \( r \)?
2. What are the solutions for \( 9 = 3r^2 \)?
3. How would you solve \( 2x^2 = 50 \) for \( x \)?
4. What is the value of \( r \) if \( 18 = 3r^2 \)?
5. How do you solve \( r^2 + 5 = 30 \) for \( r \)?

**Tip:** When taking the square root of both sides of an equation, remember to include both the positive and negative solutions.

Learn how to solve the equation 25 = 2r^2 step-by-step with detailed explanations and examples. This problem involves isolating r^2, taking square roots, and includes both positive and negative solutions. Suitable for high school students studying quadratic equations.

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