Lg^2x+lgx^2=2 help :3

[latex]lg^2x+lgx^2=2\; ;\; ODZ:\; x>0\\\\lg^2x+2lgx-2=0\\\\Zamena:\; t=lgx,\; \; \; t^2+2t-2=0\\\\D=4+8=12\\\\t_1=\frac{-2-2\sqrt3}{2}=-1-\sqrt3; \; \; t_2=-1+\sqrt3\\\\lgx=-1-\sqrt3\; \; \Rightarrow x=10^{-1-\sqrt3}\\\\lgx=-1+\sqrt3\; \; \Rightarrow \; \; x=10^{-1+\sqrt3}[/latex]