Решите уравнение: x^2+6x-2=0.

Ответ:

\[x² + 6x - 2 = 0\ \ \]

\[a = 1,\ \ b = 6,\ \ c = - 2\]

\[D = b^{2} - 4ac =\]

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

\[= 36 + 8 = 44\]

\[x_{1,2} = \frac{- b \pm \sqrt{D}}{2a}\]

\[x_{1} = \frac{- 6 + \sqrt{44}}{2 \cdot 1} = \frac{- 6 + 2\sqrt{11}}{2} =\]

\[= - 3 + \sqrt{11}\]

\[x_{2} = \frac{- 6 - \sqrt{44}}{2 \cdot 1} = \frac{- 6 - 2\sqrt{11}}{2} =\]

\[= - 3 - \sqrt{11}\]

\[Ответ:\ x = - 3 + \sqrt{11};\]

\[x = - 3 - \sqrt{11}.\]