To solve the equation \( x^2 = \frac{36}{169} \) by inspection, we can recognize that we want to find \( x \) such that \( x^2 \) equals a specific value.
We can rewrite the equation as follows:
\[ x = \sqrt{\frac{36}{169}} \quad \text{or} \quad x = -\sqrt{\frac{36}{169}} \]
Now, we can simplify the square root:
\[ \sqrt{\frac{36}{169}} = \frac{\sqrt{36}}{\sqrt{169}} = \frac{6}{13} \]
Thus, the solutions to the equation are:
\[ x = \frac{6}{13} \quad \text{or} \quad x = -\frac{6}{13} \]
So the complete solution set is:
\[ \left{ \frac{6}{13}, -\frac{6}{13} \right} \]
Since we have found real solutions, we do not need to select "There are no real solutions." The correct solution set is:
\[ \left{ \frac{6}{13}, -\frac{6}{13} \right} \]