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

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

Solve for x

$$x = \frac{18 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{93} + 9} + \sqrt[3]{9 - \sqrt{93}})}}{18} \approx 0.682327804$$

$$x=0$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+t-1=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 1 for b, and -1 for c in the quadratic formula.

$$t=\frac{-1±\sqrt{1^{2}-4\times 1\left(-1\right)}}{2}$$

Do the calculations.

$$t=\frac{-1±\sqrt{5}}{2}$$

Solve the equation t=\frac{-1±\sqrt{5}}{2} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{5}-1}{2} t=\frac{-\sqrt{5}-1}{2}$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.

$$x=\frac{\sqrt{2\sqrt{5}-2}}{2} x=-\frac{\sqrt{2\sqrt{5}-2}}{2}$$