\(2x^3+2x+x^2+1=0\\ 2x\left(x^2+1\right)+\left(x^2+1\right)=0\\ \left(x^2+1\right)\left(2x+1\right)=0\\ \left[{}\begin{matrix}x^2+1=0\\2x+1=0\end{matrix}\right.\left[{}\begin{matrix}x^2=-1\left(voli\right)\\x=-\dfrac{1}{2}\end{matrix}\right.=>x=-\dfrac{1}{2}\)