Решите уравнение: |x+6|=x^2.

\[|x + 6| = x^{2}\]

\[x + 6 = x^{2}\]

\[x^{2} - x - 6 = 0\]

\[D = ( - 1)^{2} - 4 \cdot 1 \cdot ( - 6) =\]

\[= 1 + 24 = 25\]

\[x_{1} = \frac{1 + \sqrt{25}}{2} = \frac{1 + 5}{2} = \frac{6}{2} = 3\]

\[x_{2} = \frac{1 - \sqrt{25}}{2} = \frac{1 - 5}{2} = \frac{- 4}{2} =\]

\[= - 2\]

\[x + 6 = - x^{2}\]

\[x^{2} + x + 6 = 0\]

\[D = 1^{2} - 4 \cdot 1 \cdot 6 = 1 - 24 =\]

\[= - 23 < 0\ \ нет\ решения.\]

\[Ответ:3;\ - 2.\]