The given equation is:

\[
25 = x^2 + x^2
\]

First, combine the like terms on the right-hand side:

\[
25 = 2x^2
\]

Now, divide both sides by 2 to isolate \(x^2\):

\[
x^2 = \frac{25}{2}
\]

Simplifying:

\[
x^2 = 12.5
\]

To solve for \(x\), take the square root of both sides:

\[
x = \pm \sqrt{12.5}
\]

\[
x = \pm \sqrt{12.5} \approx \pm 3.54
\]

Thus, the solution is:

\[
x \approx \pm 3.54
\]

Would you like more details or have any questions about the process?

Here are some related questions:
1. How do we combine like terms in equations?
2. How do you solve quadratic equations in general?
3. What happens if we have complex solutions?
4. How can we handle square roots of non-perfect squares?
5. Can you explain the difference between exact and approximate solutions?

**Tip:** Always check if you can simplify terms before solving an equation to make the process easier.

Learn how to solve the equation 25 = x^2 + x^2 by combining like terms and using square roots. This problem highlights key algebraic concepts such as combining terms and square root operations. Suitable for students in Grades 7-9.

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