x^3 = 338
x=
You asked:
Solve the equation \({x}^{3} = 338\) for the variable \(x\).
MathBot Answer:
The solutions are given by the formula: \[x = \sqrt[3]{338} \cos{\left(\frac{2 \pi k}{3} \right)} + \sqrt[3]{338} \sin{\left(\frac{2 \pi k}{3} \right)} i\] where \(k\) is an integer in \(0 \le k < 3\).
There is \(1\) real solution.There are \(2\) solutions with nonzero imaginary part.
Real solutions: \[\begin{aligned}x &= \sqrt[3]{338} \\&\approx 6.9658198\end{aligned}\]
Solutions with nonzero imaginary part: \[\begin{aligned}x &= - \frac{\sqrt[3]{338}}{2} + \frac{\sqrt{3} \cdot \sqrt[3]{338} i}{2} \\&\approx -3.4829099 + 6.0325769 i\\x &= - \frac{\sqrt[3]{338}}{2} - \frac{\sqrt{3} \cdot \sqrt[3]{338} i}{2} \\&\approx -3.4829099 -6.0325769 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).