[tex]x^2-4x+10y+y^2+29 = 0 \\ \\ x^2-4x+y^2+10y+4+25 = 0\\ \\ x^2-4x +4+y^2+10y+25 = 0\\ \\ \underset{\big{\geq0}}{(x-2)^2}+\underset{\big{\geq 0}}{(y+5)^2} = 0\\ ($Singurele doua numere pozitive care adunate dau zero, sunt 0+0) \\ \\ \left\{ \begin{array}{c} (x-2)^2 = 0 \\ (y+5)^2 = 0 \end{array} \right \Rightarrow \left\{ \begin{array}{c} x-2 = 0 \\ y+5 = 0 \end{array} \right \Rightarrow \left\{ \begin{array}{c} \boxed{x=2} $ $ $ $ \\ \\ \boxed{y=-5} \end{array} \right | [/tex]
