\(x^2-6x+y^2+10y+34=-\left(4z-1\right)^2\)
\(x^2-6x+9+y^2+10y+25+\left(4z-1\right)^2=0\)
\(\left(x-3\right)^2+\left(y+5\right)^2+\left(4z-1\right)^2=0\)
\(\left[\begin{array}{nghiempt}x-3=0\\y+5=0\\4z-1=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=3\\y=-5\\z=\frac{1}{4}\end{array}\right.\)