Solve x^4+x^3=500

$$x ^ { 4 } + x ^ { 3 } = 500$$

Solve for x (complex solution)

$$x=-\frac{\sqrt[3]{2}\left(1+\sqrt{3}i\right)\left(-\sqrt[3]{3\left(45\sqrt{443}+527\sqrt{3}\right)}i-\sqrt[3]{15\sqrt{1329}+527}-2\sqrt[3]{15\sqrt{1329}-527}-2\times 2^{\frac{2}{3}}+2\sqrt{3}\times 2^{\frac{2}{3}}i\right)}{12}\approx -0.248602523+4.708952094i$$

$$x = \frac{\sqrt[3]{2 {(15 \sqrt{1329} + 527)}} - \sqrt[3]{2 {(15 \sqrt{1329} - 527)}} + 4}{3} \approx 4.497205046$$

$$x=-\frac{\sqrt[3]{2}\left(-\sqrt{3}i+1\right)\left(-2\sqrt{3}\times 2^{\frac{2}{3}}i-\sqrt[3]{15\sqrt{1329}+527}-2\sqrt[3]{15\sqrt{1329}-527}-2\times 2^{\frac{2}{3}}+\sqrt[3]{3\left(45\sqrt{443}+527\sqrt{3}\right)}i\right)}{12}\approx -0.248602523-4.708952094i$$

$$x=-5$$