x^3+15x^2-12x+360=0 find x

asked by guest
on Jan 19, 2025 at 2:17 am



You asked:

Solve the equation \[{x}^{3} + 15 {x}^{2} - 12 x + 360 = 0\] for the unknown \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= -5 - \frac{87}{\sqrt[3]{9045 + 54 \sqrt{21959}}} - \frac{\sqrt[3]{9045 + 54 \sqrt{21959}}}{3} \approx -16.959247\\x &= -5 + \frac{87}{2 \sqrt[3]{54 \sqrt{21959} + 9045}} + \frac{\sqrt[3]{54 \sqrt{21959} + 9045}}{6} + i \left(- \frac{87 \sqrt{3}}{2 \sqrt[3]{54 \sqrt{21959} + 9045}} + \frac{\sqrt{3} \sqrt[3]{54 \sqrt{21959} + 9045}}{6}\right) \approx 0.97962359 + 4.5019657 i\\x &= -5 + \frac{87}{2 \sqrt[3]{54 \sqrt{21959} + 9045}} + \frac{\sqrt[3]{54 \sqrt{21959} + 9045}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{54 \sqrt{21959} + 9045}}{6} + \frac{87 \sqrt{3}}{2 \sqrt[3]{54 \sqrt{21959} + 9045}}\right) \approx 0.97962359 -4.5019657 i\end{aligned}\]

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

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