Math Problem Solver

The solutions are given by the formula: $$x = \frac{\sqrt[3]{6057608185227271128424705854} \cos{\left(\frac{2 \pi k}{3} \right)}}{111020050434} + \frac{\sqrt[3]{6057608185227271128424705854} \sin{\left(\frac{2 \pi k}{3} \right)}}{111020050434} i$$ where $k$ is an integer in $0 \le k < 3$.

There are $2$ solutions with nonzero imaginary part.

Real solutions: $$\begin{aligned}x &= \frac{\sqrt[3]{6057608185227271128424705854}}{111020050434} \\&\approx 0.016419716\end{aligned}$$

Solutions with nonzero imaginary part: $$\begin{aligned}x &= - \frac{\sqrt[3]{6057608185227271128424705854}}{222040100868} + \frac{\sqrt[3]{2019202728409090376141568618} \cdot 3^{\frac{5}{6}} i}{222040100868} \\&\approx -0.008209858 + 0.014219891 i\\x &= - \frac{\sqrt[3]{6057608185227271128424705854}}{222040100868} - \frac{\sqrt[3]{2019202728409090376141568618} \cdot 3^{\frac{5}{6}} i}{222040100868} \\&\approx -0.008209858 -0.014219891 i\end{aligned}$$

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