3x^3+6x^2-9x+63=0

asked by guest
on Nov 17, 2024 at 2:43 am



You asked:

Solve the equation \(3 \cdot {x}^{3} + 6 \cdot {x}^{2} - 9 x + 63 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{2}{3} - \frac{13}{3 \sqrt[3]{\frac{637}{2} + \frac{117 \sqrt{29}}{2}}} - \frac{\sqrt[3]{\frac{637}{2} + \frac{117 \sqrt{29}}{2}}}{3} \approx -4.0340809\\x &= - \frac{2}{3} + \frac{13}{6 \sqrt[3]{\frac{117 \sqrt{29}}{2} + \frac{637}{2}}} + \frac{\sqrt[3]{\frac{117 \sqrt{29}}{2} + \frac{637}{2}}}{6} + i \left(- \frac{13 \sqrt{3}}{6 \sqrt[3]{\frac{117 \sqrt{29}}{2} + \frac{637}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{117 \sqrt{29}}{2} + \frac{637}{2}}}{6}\right) \approx 1.0170404 + 2.0423701 i\\x &= - \frac{2}{3} + \frac{13}{6 \sqrt[3]{\frac{117 \sqrt{29}}{2} + \frac{637}{2}}} + \frac{\sqrt[3]{\frac{117 \sqrt{29}}{2} + \frac{637}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{117 \sqrt{29}}{2} + \frac{637}{2}}}{6} + \frac{13 \sqrt{3}}{6 \sqrt[3]{\frac{117 \sqrt{29}}{2} + \frac{637}{2}}}\right) \approx 1.0170404 -2.0423701 i\end{aligned}\]

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

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