The inequality \( x^2 \leq 25 \) can be solved as follows:

### Step 1: Solve the equality
First, solve the equation \( x^2 = 25 \).

\[
x^2 = 25 \quad \Rightarrow \quad x = \pm \sqrt{25}
\]
\[
x = \pm 5
\]

### Step 2: Solve the inequality
Now, consider the inequality \( x^2 \leq 25 \). This means that the value of \( x \) lies between the square roots of \( 25 \).

\[
-5 \leq x \leq 5
\]

Thus, the solution is:

\[
x \in [-5, 5]
\]

### Final Answer:
The solution to the inequality is \( x \in [-5, 5] \).

Would you like further details or have any questions?

Here are some related questions you could explore:
1. How would the solution change for \( x^2 < 25 \)?
2. How would you solve \( x^2 \geq 16 \)?
3. What is the solution to \( x^2 > 9 \)?
4. How can you solve an inequality like \( (x - 2)^2 \leq 16 \)?
5. What happens if you solve \( x^4 \leq 81 \)?

**Tip**: When solving inequalities involving squares, don't forget to consider both positive and negative roots.

Discover how to solve the quadratic inequality x^2 <= 25 step by step. This problem involves solving quadratic equations and applying the properties of inequalities, suitable for students in Grades 8-10.

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