Решите уравнение х^2+у^2+10х+6у+34=0.

\[x^{2} + y^{2} + 10x + 6y + 34 = 0\]

\[x^{2} + 10x + 25 + y^{2} + 6y + 9 = 0\]

\[(x + 5)^{2} + (y + 3)^{2} = 0\]

\[x + 5 = 0\ \ \ \ \ \ \ \ \ \ y + 3 = 0\]

\[x = - 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ y = - 3\]

\[Ответ:( - 5;\ - 3).\]