\(\sqrt{x^2-10x+25}=17\)
\(\Leftrightarrow\sqrt{\left(x-5\right)^2}=17\)
\(\Leftrightarrow\left|x-5\right|=17\)
\(\left|x-5\right|=\left\{{}\begin{matrix}x-5khix\ge5\\-x+5khix< 5\end{matrix}\right.\)
Với \(x\ge5\Rightarrow x-5=17\Rightarrow x=22\left(tm\right)\)
Với \(x< 5\Rightarrow-x+5=17\Rightarrow x=-12\left(tm\right)\)
Vậy \(S=\left\{22;-12\right\}\)