Example 10. Solve the equation

$$
\sqrt{x+16}-x+4=0
$$
Solution. The domain of the equation: $x \geqslant-16$. Isolating the radical, we get the equation $\sqrt{x+16}=x-4$. Squaring both sides of this equation and combining like terms, we obtain the equation $x^{2}-9 x=0$, the roots of which are: $x_{1}=0$ and $x_{2}=9$. Each of these roots belongs to the domain of the original equation.

For the root $x_{1}=0$, the parts of the equation $\sqrt{x+16}=x-4$ being squared have different signs; therefore, $x_{1}=0$ is an extraneous root of the original equation.

By substitution, we verify that $x=9$ is the only root of the original equation.