To solve the equation \( x^2 = \frac{36}{169} \) using inspection, we need to find values of \( x \) that satisfy this equation.
First, we take the square root of both sides:
\[ x = \pm \sqrt{\frac{36}{169}} \]
Next, we simplify the right side:
\[ \sqrt{\frac{36}{169}} = \frac{\sqrt{36}}{\sqrt{169}} = \frac{6}{13} \]
Therefore, the solutions for \( x \) are:
\[ x = \frac{6}{13} \quad \text{and} \quad x = -\frac{6}{13} \]
Thus, the solution set is:
\[ \left{ \frac{6}{13}, -\frac{6}{13} \right} \]