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

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

Solve for x

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

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

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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

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

Do the calculations.

$$t=\frac{6±2}{4}$$

Solve the equation t=\frac{6±2}{4} 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.

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