Решите уравнение: |x^2+11x-6|=6.

\[\left| x^{2} + 11x - 6 \right| = 6\]

\[x^{2} + 11x - 12 = 0\]

\[D = 11^{2} - 4 \cdot 1 \cdot ( - 12) =\]

\[= 121 + 48 = 169\]

\[x_{1} = \frac{- 11 + \sqrt{169}}{2} =\]

\[= \frac{- 11 + 13}{2} = \frac{2}{2} = 1\]

\[x_{2} = \frac{- 11 - \sqrt{169}}{2} =\]

\[= \frac{- 11 - 13}{2} = - \frac{24}{2} = - 12\]

\[x^{2} + 11x = 0\]

\[x(x + 11) = 0\]

\[x = 0\ \ \ \ \ \ \ \ \ \ x + 11 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 11\]

\[Ответ:x = 1;\ x = - 12;x = 0;\ \]

\[x = - 11.\]