\(x^2+y^2+6x-10y+34=0\)
\(\Leftrightarrow x^2+6x+9+y^2-10y+25=0\)
\(\Leftrightarrow\left(x+3\right)^2+\left(x-5\right)^2=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+3=0\\x-5=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-3\\x=5\end{cases}}\)
Vậy \(S=\left\{-3;5\right\}\)
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