[tex]a)\quad \sqrt{(x+5)^2} = 11\\ \\ \Leftrightarrow\,|x+5| = 11 \\ \\\Leftrightarrow\,x+5 = 11\quad \vee\quad x+5 = -11\\ \\ \Leftrightarrow\, x = 11-5\quad \vee\quad x = -11-5 \\ \\ \Leftrightarrow\, x = 6\quad \vee\quad x = -16\\ \\ \Rightarrow \, \boxed{x\in \left\{-16;\, 6\right\}}[/tex]
