Решите уравнение: x|x|+8x-7=0.

\[x|x| + 8x - 7 = 0\]

\[D = 8^{2} - 4 \cdot 1 \cdot ( - 7) =\]

\[= 64 + 28 = 92\]

\[x_{1} = \frac{- 8 + \sqrt{92}}{2} = \frac{- 8 + 2\sqrt{23}}{2} =\]

\[= - 4 + \sqrt{23}\]

\[x_{2} = \frac{- 8 - \sqrt{92}}{2} = \frac{- 8 - 2\sqrt{23}}{2} =\]

\[= - 4 - \sqrt{23}\ (не\ подходит).\]

\[D = 8^{2} - 4 \cdot ( - 1) \cdot ( - 7) =\]

\[= 64 - 28 = 36\]

\[x_{1} = \frac{- 8 + \sqrt{36}}{2 \cdot ( - 1)} = \frac{- 8 + 6}{- 2} =\]

\[= \frac{- 2}{- 2} = 1\ (не\ подходит)\]

\[x_{2} = \frac{- 8 - \sqrt{36}}{2 \cdot ( - 1)} = \frac{- 8 - 6}{- 2} =\]

\[= \frac{- 14}{- 2} = 7\ (не\ подходит).\]

\[Ответ:\ - 4 + \sqrt{23}.\]