To solve the equation \( x^2 = 88.3769208100000 \), we take the square root of both sides.
\[ x = \sqrt{88.3769208100000} \]
Now, let's calculate the square root:
\[ x \approx 9.4 \quad \text{(when rounded to the nearest tenth)} \]
So, the final answer is:
\[ \boxed{9.4} \]