(x+2)(x^3/2-8)=0
You asked:
Solve the equation \(\left(x + 2\right) \left(\frac{{x}^{3}}{2} - 8\right) = 0\) for the variable \(x\).
MathBot Answer:
The 4 solutions to the equation are: \[\begin{aligned}x &= -2\\x &= 2 \cdot \sqrt[3]{2} \approx 2.5198421\\x &= - \sqrt[3]{2} + \sqrt[3]{2} \sqrt{3} i \approx -1.259921 + 2.1822473 i\\x &= - \sqrt[3]{2} - \sqrt[3]{2} \sqrt{3} i \approx -1.259921 -2.1822473 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).