3*x - x^3 + 6.6 = 0

asked by guest
on Nov 14, 2024 at 9:11 am



You asked:

Solve the equation \(3 x - {x}^{3} + 6.6 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \frac{1}{\sqrt[3]{\frac{33}{10} + \frac{\sqrt{989}}{10}}} + \sqrt[3]{\frac{33}{10} + \frac{\sqrt{989}}{10}} \approx 2.3983179\\x &= - \frac{\sqrt[3]{\frac{\sqrt{989}}{10} + \frac{33}{10}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{989}}{10} + \frac{33}{10}}} + i \left(- \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{989}}{10} + \frac{33}{10}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{989}}{10} + \frac{33}{10}}}{2}\right) \approx -1.199159 + 1.1462751 i\\x &= - \frac{\sqrt[3]{\frac{\sqrt{989}}{10} + \frac{33}{10}}}{2} - \frac{1}{2 \sqrt[3]{\frac{\sqrt{989}}{10} + \frac{33}{10}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{989}}{10} + \frac{33}{10}}}{2} + \frac{\sqrt{3}}{2 \sqrt[3]{\frac{\sqrt{989}}{10} + \frac{33}{10}}}\right) \approx -1.199159 -1.1462751 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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