To solve the equation \( x^2 = \frac{16}{25} \) by inspection, we can look for values of \( x \) that, when squared, yield \( \frac{16}{25} \).
We recognize that:
\[ \left(\frac{4}{5}\right)^2 = \frac{4^2}{5^2} = \frac{16}{25} \]
Thus, one solution is \( x = \frac{4}{5} \).
Since squaring a negative number also results in a positive outcome, we should also consider the negative solution:
\[ \left(-\frac{4}{5}\right)^2 = \frac{16}{25} \]
Therefore, the solutions to the equation \( x^2 = \frac{16}{25} \) are:
\[ x = \frac{4}{5} \quad \text{and} \quad x = -\frac{4}{5} \]