To solve the equation \(3^2 + x^2 = 15^2\), we start by calculating the squares of the numbers:
\[ 3^2 = 9 \] \[ 15^2 = 225 \]
Now, substitute these values back into the equation:
\[ 9 + x^2 = 225 \]
Next, we isolate \(x^2\) by subtracting 9 from both sides:
\[ x^2 = 225 - 9 \] \[ x^2 = 216 \]
Now, take the square root of both sides to solve for \(x\):
\[ x = \pm \sqrt{216} \]
The square root of 216 can be simplified:
\[ \sqrt{216} = \sqrt{36 \times 6} = \sqrt{36} \times \sqrt{6} = 6\sqrt{6} \]
Thus, the solutions for \(x\) are:
\[ x = 6\sqrt{6} \quad \text{or} \quad x = -6\sqrt{6} \]
So, the final solutions are:
\[ x = \pm 6\sqrt{6} \]