$\left\{ {\begin{array}{*{20}{c}}{x + y = 2 \Rightarrow y = 2 - x}\\{xy =  - 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.$ $ \Rightarrow x(2 - x) =  - 4 \Rightarrow  - {x^2} + 2x + 4 = 0 \Rightarrow {x^2} - 2x - 4 = 0$$\Delta  = 4 - 4(1)( - 4) = 20$${x_1} = \frac{{2 - \sqrt {20} }}{2} = \frac{{2 - \sqrt {4 \times 5} }}{2} = \frac{{2 - 2\sqrt 5 }}{2} = 1 - \sqrt 5 $${x_2} = \frac{{2 + \sqrt {20} }}{2} = \frac{{2 + \sqrt {4 \times 5} }}{2} = \frac{{2 + 2\sqrt 5 }}{2} = 1 + \sqrt 5 $