50x^3+56250x^2-8437524x+421875000=0

asked by guest
on Nov 27, 2024 at 5:30 pm



You asked:

Solve the equation \(50 {x}^{3} + 56250 {x}^{2} - 8437524 x + 421875000 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= -375 - \frac{14765637}{50 \sqrt[3]{299004210 + \frac{27 \sqrt{3406578497204765561}}{1000}}} - \frac{2 \sqrt[3]{299004210 + \frac{27 \sqrt{3406578497204765561}}{1000}}}{3} \approx -1263.8081\\x &= -375 + \frac{14765637}{100 \sqrt[3]{\frac{27 \sqrt{3406578497204765561}}{1000} + 299004210}} + \frac{\sqrt[3]{\frac{27 \sqrt{3406578497204765561}}{1000} + 299004210}}{3} + i \left(- \frac{14765637 \sqrt{3}}{100 \sqrt[3]{\frac{27 \sqrt{3406578497204765561}}{1000} + 299004210}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{3406578497204765561}}{1000} + 299004210}}{3}\right) \approx 69.404025 + 43.119978 i\\x &= -375 + \frac{14765637}{100 \sqrt[3]{\frac{27 \sqrt{3406578497204765561}}{1000} + 299004210}} + \frac{\sqrt[3]{\frac{27 \sqrt{3406578497204765561}}{1000} + 299004210}}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{3406578497204765561}}{1000} + 299004210}}{3} + \frac{14765637 \sqrt{3}}{100 \sqrt[3]{\frac{27 \sqrt{3406578497204765561}}{1000} + 299004210}}\right) \approx 69.404025 -43.119978 i\end{aligned}\]

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

+ Submit Question