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

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

Solve for x

$$x=-2$$

$$x=2$$

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

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

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

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

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.

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

Do the calculations.

$$t=\frac{6±2}{2}$$

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

$$t=4 t=2$$

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

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