Solve 8x^4-18x^2+4=0

$$8 x ^ { 4 } - 18 x ^ { 2 } + 4 = 0$$

Solve for x

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

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

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$8t^{2}-18t+4=0$$

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 8 for a, -18 for b, and 4 for c in the quadratic formula.

$$t=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 8\times 4}}{2\times 8}$$

Do the calculations.

$$t=\frac{18±14}{16}$$

Solve the equation t=\frac{18±14}{16} when ± is plus and when ± is minus.

$$t=2 t=\frac{1}{4}$$

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

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