\[\boxed{\text{1277.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[x^{2} + 12x + 30 = 0\]
\[D_{1} = 36 - 30 = 6\]
\[x_{1} = - 6 + \sqrt{6};\ \ x_{2} = - 6 - \sqrt{6}.\]
\[\left( - 6 + \sqrt{6} \right)^{2} + \left( - 6 - \sqrt{6} \right)^{2} =\]
\[= 6 - 12\sqrt{6} + 36 + 6 +\]
\[+ 12\sqrt{6} + 36 = 84.\]
\[Ответ:84.\]