Решите уравнение 49x^3+14x^2+x=0.

\[49x^{3} + 14x^{2} + x = 0\]

\[x\left( 49x^{2} + 14x + 1 \right) = 0\]

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

\[x = 0;\ \ \ \ \ 7x + 1 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7x = - 1\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{1}{7}\]

\[Ответ:x = - \frac{1}{7};\ \ x = 0.\]