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.