352x^3=1188
You asked:
Solve the equation \(352 {x}^{3} = 1188\) for the variable \(x\).
MathBot Answer:
The solutions are given by the formula: \[x = \frac{3 \cos{\left(\frac{2 \pi k}{3} \right)}}{2} + \frac{3 \sin{\left(\frac{2 \pi k}{3} \right)}}{2} i\] 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: \[\begin{aligned}x &= \frac{3}{2} \\&= 1.5\end{aligned}\]
Solutions with nonzero imaginary part: \[\begin{aligned}x &= - \frac{3}{4} + \frac{3 \sqrt{3} i}{4} \\&\approx -0.75 + 1.2990381 i\\x &= - \frac{3}{4} - \frac{3 \sqrt{3} i}{4} \\&\approx -0.75 -1.2990381 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).