Solve x^4-5x^2+y=0

$$x ^ { 4 } - 5 x ^ { 2 } + y = 0$$

Solve for y

$$y=-x^{2}\left(x^{2}-5\right)$$

Solution Steps

Subtract x^{4} from both sides. Anything subtracted from zero gives its negation.

$$-5x^{2}+y=-x^{4}$$

Add 5x^{2} to both sides.

$$y=-x^{4}+5x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{-2\sqrt{25-4y}+10}}{2}$$

$$x=-\frac{\sqrt{-2\sqrt{25-4y}+10}}{2}$$

$$x=-\frac{\sqrt{2\sqrt{25-4y}+10}}{2}$$

$$x=\frac{\sqrt{2\sqrt{25-4y}+10}}{2}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{2\sqrt{25-4y}+10}}{2}\text{; }x=\frac{\sqrt{2\sqrt{25-4y}+10}}{2}\text{, }&y\leq \frac{25}{4}\\x=-\frac{\sqrt{-2\sqrt{25-4y}+10}}{2}\text{; }x=\frac{\sqrt{-2\sqrt{25-4y}+10}}{2}\text{, }&y\geq 0\text{ and }y\leq \frac{25}{4}\end{matrix}\right.$$