$\begin{array}{l} x_1^2 + 2{x_1}{x_2} + {x_2} = 1\\ \Leftrightarrow x_1^2 + 2{x_1}\left( { - 1 - {x_1}} \right) + \left( { - 1 - {x_1}} \right) = 1\\ \Leftrightarrow x_1^2 - 2{x_1} - 2x_1^2 - 1 - {x_1} - 1 = 0\\ \Leftrightarrow x_1^2 + 3{x_1} + 2 = 0\\ \Leftrightarrow \left( {{x_1} + 1} \right)\left( {{x_1} + 2} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} {x_1} = - 1 \Rightarrow {x_2} = 0\\ {x_1} = - 2 \Rightarrow {x_2} = 1 \end{array} \right. \end{array}$
