Solve 6x^4+5x^2+1=0

$$6 x ^ { 4 } + 5 x ^ { 2 } + 1 = 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{2}i}{2}\approx 0.707106781i$$

$$x=-\frac{\sqrt{2}i}{2}\approx -0-0.707106781i$$

$$x=-\frac{\sqrt{3}i}{3}\approx -0-0.577350269i$$

$$x=\frac{\sqrt{3}i}{3}\approx 0.577350269i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$6t^{2}+5t+1=0$$

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 6 for a, 5 for b, and 1 for c in the quadratic formula.

$$t=\frac{-5±\sqrt{5^{2}-4\times 6\times 1}}{2\times 6}$$

Do the calculations.

$$t=\frac{-5±1}{12}$$

Solve the equation t=\frac{-5±1}{12} when ± is plus and when ± is minus.

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

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

$$x=-\frac{\sqrt{3}i}{3} x=\frac{\sqrt{3}i}{3} x=-\frac{\sqrt{2}i}{2} x=\frac{\sqrt{2}i}{2}$$