Solve x=y^2+0.5y-sqrt{-4}*y^3

$$x = y ^ { 2 } + 0.5 y - \sqrt { - 4 } \cdot y ^ { 3 }$$

Solve for x

$$x=y\left(0.5+y-2iy^{2}\right)$$

Solution Steps

Calculate the square root of -4 and get 2i.

$$x=y^{2}+0.5y-2iy^{3}$$

Solve for y

$$y=-\frac{\sqrt[3]{2}\left(1+i\sqrt{3}\right)\left(3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)\right)^{-\frac{1}{3}}\left(\sqrt[3]{2}\left(-\left(3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)\right)^{\frac{2}{3}}+\sqrt[3]{2}\left(\sqrt[3]{3\left(9\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108i\sqrt{3}x+\left(-9+2i\right)\sqrt{3}\right)}+i\sqrt[3]{3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)}\right)\right)-i\sqrt[3]{2\left(3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)\right)}\sqrt[3]{3\left(9\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108i\sqrt{3}x+\left(-9+2i\right)\sqrt{3}\right)}+\left(-4-12i\right)\right)}{48}$$

$$y=\frac{2^{\frac{2}{3}}\left(3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)\right)^{-\frac{1}{3}}\left(\left(3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)\right)^{\frac{2}{3}}+\sqrt[3]{2}\left(-i\sqrt[3]{3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)}+\left(-1-3i\right)\sqrt[3]{2}\right)\right)}{12}$$

$$y=-\frac{\sqrt[3]{2}\left(-i\sqrt{3}+1\right)\left(3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)\right)^{-\frac{1}{3}}\left(\sqrt[3]{2}\left(-\left(3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)\right)^{\frac{2}{3}}+\sqrt[3]{2}\left(-\sqrt[3]{3\left(9\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108i\sqrt{3}x+\left(-9+2i\right)\sqrt{3}\right)}+i\sqrt[3]{3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)}\right)\right)+i\sqrt[3]{2\left(3\sqrt{3}\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108ix+\left(-9+2i\right)\right)}\sqrt[3]{3\left(9\sqrt{-1-4i+\left(-16-72i\right)x-432x^{2}}+108i\sqrt{3}x+\left(-9+2i\right)\sqrt{3}\right)}+\left(-4-12i\right)\right)}{48}$$