1. (17 points) Solve the equation $12 x=\sqrt{36+x^{2}}\left(6+x-\sqrt{36+x^{2}}\right)$.
Answer: $-6 ; 0$.

Solution. Transform the equation to the form $x^{2}+12 x+36=\sqrt{36+x^{2}}(6+x)$. After completing the square and factoring, we get the equation

$$
(x+6)\left(x+6-\sqrt{36+x^{2}}\right)=0 \Leftrightarrow\left[\begin{array}{c}
x+6=0 \\
x+6=\sqrt{36+x^{2}}
\end{array}\right.
$$

from the obtained equations, we find: $x=-6, x=0$.