Решите уравнение: |x-6|=x^2.

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

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

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

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

\[= 1 - 24 = - 23 < 0 \Longrightarrow \ \]

\[\Longrightarrow \ нет\ решения.\]

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

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

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

\[= 1 + 24 = 25\]

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

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

\[= \frac{- 6}{2} = - 3\]

\[Ответ:2;\ - 3.\]