Решите уравнение х^2+у^2+34=6х-10у.

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

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

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

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

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

\[Ответ:x = 3;\ \ y = - 5.\]