To solve the equation \(3^2 + x^2 = 15^2\), we'll first calculate the values of \(3^2\) and \(15^2\).
\[ 3^2 = 9 \]
\[ 15^2 = 225 \]
Now, substituting these values into the equation gives us:
\[ 9 + x^2 = 225 \]
Next, we will isolate \(x^2\) by subtracting \(9\) from both sides:
\[ x^2 = 225 - 9 \]
\[ x^2 = 216 \]
Now, we take the square root of both sides to solve for \(x\):
\[ x = \sqrt{216} \]
Calculating \(\sqrt{216}\):
\[ \sqrt{216} \approx 14.7\text{ (rounded to the nearest tenth)} \]
So, the value of \(x\) rounded to the nearest tenth is:
\[ \boxed{14.7} \]