Math Problem Solver

The solutions are given by the formula: $$x = \frac{10^{\frac{2}{3}} \cos{\left(\frac{2 \pi k}{3} \right)}}{10} + \frac{10^{\frac{2}{3}} \sin{\left(\frac{2 \pi k}{3} \right)}}{10} i$$ where $k$ is an integer in $0 \le k < 3$.

There are $2$ solutions with nonzero imaginary part.

Real solutions: $$\begin{aligned}x &= \frac{10^{\frac{2}{3}}}{10} \\&\approx 0.46415888\end{aligned}$$

Solutions with nonzero imaginary part: $$\begin{aligned}x &= - \frac{10^{\frac{2}{3}}}{20} + \frac{10^{\frac{2}{3}} \sqrt{3} i}{20} \\&\approx -0.23207944 + 0.40197338 i\\x &= - \frac{10^{\frac{2}{3}}}{20} - \frac{10^{\frac{2}{3}} \sqrt{3} i}{20} \\&\approx -0.23207944 -0.40197338 i\end{aligned}$$

$i$ is the imaginary unit, defined as $i^2 = -1$.