$$x^3+x = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = i & x_3 = -i \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ x^{3}+x = 0 } $, first we need to factor our $ x $.
$$ x^{3}+x = x \left( x^{2}+1 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ x^{2}+1 = 0$.
$ x^{2}+1 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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