Solve 3x^4+x^2-2=0

$$3 x ^ { 4 } + x ^ { 2 } - 2 = 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$3t^{2}+t-2=0$$

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 3 for a, 1 for b, and -2 for c in the quadratic formula.

$$t=\frac{-1±\sqrt{1^{2}-4\times 3\left(-2\right)}}{2\times 3}$$

Do the calculations.

$$t=\frac{-1±5}{6}$$

Solve the equation t=\frac{-1±5}{6} when ± is plus and when ± is minus.

$$t=\frac{2}{3} t=-1$$

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

$$x=-\frac{\sqrt{6}}{3} x=\frac{\sqrt{6}}{3} x=-i x=i$$

Solve for x

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$3t^{2}+t-2=0$$

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 3 for a, 1 for b, and -2 for c in the quadratic formula.

$$t=\frac{-1±\sqrt{1^{2}-4\times 3\left(-2\right)}}{2\times 3}$$

Do the calculations.

$$t=\frac{-1±5}{6}$$

Solve the equation t=\frac{-1±5}{6} when ± is plus and when ± is minus.

$$t=\frac{2}{3} t=-1$$

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

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$