1. (17 points) Solve the equation $10 x=\sqrt{25+x^{2}}\left(5+x-\sqrt{25+x^{2}}\right)$.
Answer: $-5 ; 0$.

Solution. Transform the equation to the form $x^{2}+10 x+25=\sqrt{25+x^{2}}(5+x)$.

After completing the square and factoring, we get the equation $\quad(x+5)\left(x+5-\sqrt{25+x^{2}}\right)=0 \Leftrightarrow\left[\begin{array}{c}x+5=0, \\ x+5=\sqrt{25+x^{2}} .\end{array}\right.$ From the obtained equations, we find: $x=-5, x=0$.