\[\sqrt{x^{2}} = x + 10\]
\[|x| = x + 10\]
\[x = x + 10,\ \ x = - x - 10\]
\[0 = 10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x = - 10\]
\[нет\ решения\ \ \ \ \ x = - 5\]
\[Ответ:\ x = - 5.\]