Solve -x^4-6x^2+8=0

$$- x ^ { 4 } - 6 x ^ { 2 } + 8 = 0$$

Solve for x (complex solution)

$$x=i\sqrt{\sqrt{17}+3}\approx 2.668914691i$$

$$x=-i\sqrt{\sqrt{17}+3}\approx -0-2.668914691i$$

$$x=-\sqrt{\sqrt{17}-3}\approx -1.059766779$$

$$x=\sqrt{\sqrt{17}-3}\approx 1.059766779$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-t^{2}-6t+8=0$$

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 8 for c in the quadratic formula.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\times 8}}{-2}$$

Do the calculations.

$$t=\frac{6±2\sqrt{17}}{-2}$$

Solve the equation t=\frac{6±2\sqrt{17}}{-2} when ± is plus and when ± is minus.

$$t=-\sqrt{17}-3 t=\sqrt{17}-3$$

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

$$x=-i\sqrt{\sqrt{17}+3} x=i\sqrt{\sqrt{17}+3} x=-\sqrt{\sqrt{17}-3} x=\sqrt{\sqrt{17}-3}$$

Solve for x

$$x=-\sqrt{\sqrt{17}-3}\approx -1.059766779$$

$$x=\sqrt{\sqrt{17}-3}\approx 1.059766779$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-t^{2}-6t+8=0$$

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 8 for c in the quadratic formula.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\times 8}}{-2}$$

Do the calculations.

$$t=\frac{6±2\sqrt{17}}{-2}$$

Solve the equation t=\frac{6±2\sqrt{17}}{-2} when ± is plus and when ± is minus.

$$t=-\sqrt{17}-3 t=\sqrt{17}-3$$

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

$$x=\sqrt{\sqrt{17}-3} x=-\sqrt{\sqrt{17}-3}$$