x^3+2x^2+2x = 3240

asked by guest
on Nov 21, 2024 at 1:54 am



You asked:

Solve the equation \({x}^{3} + 2 \cdot {x}^{2} + 2 x = 3240\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{2}{3} + \sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}} - \frac{2}{9 \sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}} \approx 14.116717\\x &= - \frac{\sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}}{2} - \frac{2}{3} + \frac{1}{9 \sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}} + i \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}} + \frac{\sqrt{3} \sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}}{2}\right) \approx -8.0583584 + 12.828795 i\\x &= - \frac{\sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}}{2} - \frac{2}{3} + \frac{1}{9 \sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}}{2} - \frac{\sqrt{3}}{9 \sqrt[3]{\frac{43750}{27} + \frac{2 \sqrt{53168403}}{9}}}\right) \approx -8.0583584 -12.828795 i\end{aligned}\]

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

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