The equation you provided is:

\[
x^2 - 16 = 9
\]

### Step 1: Isolate \(x^2\)
First, move the 9 to the other side of the equation:

\[
x^2 - 16 - 9 = 0
\]
\[
x^2 - 25 = 0
\]

### Step 2: Solve for \(x^2\)
Now, add 25 to both sides to isolate \(x^2\):

\[
x^2 = 25
\]

### Step 3: Solve for \(x\)
Take the square root of both sides:

\[
x = \pm \sqrt{25}
\]
\[
x = \pm 5
\]

### Final Answer:
The solution is:

\[
x = 5 \quad \text{or} \quad x = -5
\]

Would you like more details or have any questions?

Here are some related questions:
1. What happens if the equation has a cube instead of a square?
2. How do you solve a quadratic equation with a linear term?
3. What if the equation is \(x^2 - 25 = -9\)?
4. Can you explain how to solve \(x^2 - 16 = 0\)?
5. How would you factor \(x^2 - 25\)?

**Tip:** Always double-check your solutions by substituting them back into the original equation to ensure they satisfy it.

This detailed solution walks you through solving the quadratic equation X^2 - 16 = 9. Learn how to isolate x^2 and solve for x using square roots. This algebra problem is suitable for students in Grades 7-9, covering core concepts of quadratic equations and square roots.

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