\[x^{2} + 10x - 4 = 0\]
\[x_{1} + x_{2} = - 10;\ \ \ \ \ x_{1} \cdot x_{2} = - 4:\]
\[x_{1}^{2} + x_{2}^{2} = \left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2} =\]
\[= ( - 10)^{2} - 2 \cdot ( - 4) = 100 + 8 = 108.\]
\[Ответ:108.\]