Решите уравнение: 2x^3+7x^2+7x+2=0.

\[2x^{3} + 7x^{2} + 7x + 2 = 0\]

\[2 \bullet \left( x^{3} + 1 \right) + 7x(x + 1) = 0\]

\[(x + 1)\left( 2x^{2} - 2x + 2 + 7x \right) = 0\]

\[x + 1 = 0 \Longrightarrow x = - 1.\]

\[2x^{2} + 5x + 2 = 0\]

\[D = 5^{2} - 4 \cdot 2 \cdot 2 = 25 - 16 = 9\]

\[x_{1} = \frac{- 5 + \sqrt{9}}{2 \cdot 2} = \frac{- 5 + 3}{4} = \frac{- 2}{4} =\]

\[= - \frac{1}{2}\]

\[x_{2} = \frac{- 5 - \sqrt{9}}{2 \cdot 2} = \frac{- 5 - 3}{4} = \frac{- 8}{4} =\]

\[= - 2\]

\[Ответ:\ x = - 1;\ x = - 0,5;\ \]

\[x = - 2.\]