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

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

Solve for x (complex solution)

$$x=1$$

$$x=-1$$

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

$$x=\sqrt{2}i\approx 1.414213562i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-4t^{2}-4t+8=0$$

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 -4 for a, -4 for b, and 8 for c in the quadratic formula.

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

Do the calculations.

$$t=\frac{4±12}{-8}$$

Solve the equation t=\frac{4±12}{-8} when ± is plus and when ± is minus.

$$t=-2 t=1$$

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

$$x=-\sqrt{2}i x=\sqrt{2}i x=-1 x=1$$

Solve for x

$$x=-1$$

$$x=1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-4t^{2}-4t+8=0$$

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 -4 for a, -4 for b, and 8 for c in the quadratic formula.

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

Do the calculations.

$$t=\frac{4±12}{-8}$$

Solve the equation t=\frac{4±12}{-8} when ± is plus and when ± is minus.

$$t=-2 t=1$$

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

$$x=1 x=-1$$