\eqalign{ & x + 2\sqrt x = 8 \cr & 2\sqrt x = - x + 8 \cr & 4x = ( - x + 8)^2 \cr & 4x = x^2 - 16x + 64 \cr & x^2 - 20x + 64 = 0 \cr & (x - 4)(x - 16) = 0 \cr & x = 4 \vee x = 16\,\,(v.n.) \cr & x = 4 \cr}
\eqalign{ & \sqrt {x^2 - 4} + x + 2 = 0 \cr & \sqrt {x^2 - 4} = - x - 2 \cr & x^2 - 4 = ( - x - 2)^2 \cr & x^2 - 4 = x^2 + 4x + 4 \cr & - 4 = 4x + 4 \cr & 4x = - 8 \cr & x = - 2 \cr}