Solve x^4+6x^2+4=0

$${ x }^{ 4 } +6 { x }^{ 2 } +4=0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{2}i+\sqrt{10}i}{2}\approx 2.288245611i$$

$$x=\frac{-\sqrt{2}i-\sqrt{10}i}{2}\approx -2.288245611i$$

$$x=\frac{\sqrt{2}i-\sqrt{10}i}{2}\approx -0.874032049i$$

$$x=\frac{\sqrt{10}i-\sqrt{2}i}{2}\approx 0.874032049i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+6t+4=0$$

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, 6 for b, and 4 for c in the quadratic formula.

$$t=\frac{-6±\sqrt{6^{2}-4\times 1\times 4}}{2}$$

Do the calculations.

$$t=\frac{-6±2\sqrt{5}}{2}$$

Solve the equation t=\frac{-6±2\sqrt{5}}{2} when ± is plus and when ± is minus.

$$t=\sqrt{5}-3 t=-\sqrt{5}-3$$

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

$$x=\frac{\sqrt{2}i-\sqrt{10}i}{2} x=-\frac{\sqrt{2}i-\sqrt{10}i}{2} x=-\frac{\sqrt{2}i+\sqrt{10}i}{2} x=\frac{\sqrt{2}i+\sqrt{10}i}{2}$$