Math Problem Solver

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{44}{15} - \frac{2 \sqrt{946} \cos{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{15} \approx -6.7975164\\x &= - \frac{44}{15} - \frac{\sqrt{2838} \sin{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{30} - \frac{946 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{15119}{125} + \frac{21 \sqrt{56055} i}{25}}}\right)}}{75} + \frac{\sqrt{946} \cos{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{30} + i \left(- \frac{946 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{15119}{125} + \frac{21 \sqrt{56055} i}{25}}}\right)}}{75} + \frac{\sqrt{946} \sin{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{30} + \frac{\sqrt{2838} \cos{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{30}\right) \approx -2.1905274 -1.0 \cdot 10^{-143} i\\x &= - \frac{44}{15} + \frac{\sqrt{2838} \sin{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{30} + \frac{\sqrt{946} \cos{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{30} - \frac{946 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{15119}{125} + \frac{21 \sqrt{56055} i}{25}}}\right)}}{75} + i \left(- \frac{\sqrt{2838} \cos{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{30} + \frac{\sqrt{946} \sin{\left(\frac{\arctan{\left(\frac{105 \sqrt{56055}}{15119} \right)}}{3} \right)}}{30} - \frac{946 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{15119}{125} + \frac{21 \sqrt{56055} i}{25}}}\right)}}{75}\right) \approx 0.18804382 + 7.0 \cdot 10^{-142} i\end{aligned}\]

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