find the value of x: 2x^3 - 5x^2 + 3x - 7 + 8x = 0

asked by guest
on Nov 18, 2024 at 3:41 am



You asked:

Solve the equation \[2 \cdot {x}^{3} - 5 \cdot {x}^{2} + 3 x - 7 + 8 x = 0\] for the unknown \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \frac{5}{6} + \sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}} - \frac{41}{36 \sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}} \approx 0.85501057\\x &= - \frac{\sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}}{2} + \frac{41}{72 \sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}} + \frac{5}{6} + i \left(\frac{41 \sqrt{3}}{72 \sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}}{2}\right) \approx 0.82249472 + 1.8485181 i\\x &= - \frac{\sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}}{2} + \frac{41}{72 \sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}} + \frac{5}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}}{2} - \frac{41 \sqrt{3}}{72 \sqrt[3]{\frac{1}{27} + \frac{\sqrt{7665}}{72}}}\right) \approx 0.82249472 -1.8485181 i\end{aligned}\]

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

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