Solve 6x^4-7x^2+2=0

$$6 x ^ { 4 } - 7 x ^ { 2 } + 2 = 0$$

Solve for x

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$6t^{2}-7t+2=0$$

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 6 for a, -7 for b, and 2 for c in the quadratic formula.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 6\times 2}}{2\times 6}$$

Do the calculations.

$$t=\frac{7±1}{12}$$

Solve the equation t=\frac{7±1}{12} when ± is plus and when ± is minus.

$$t=\frac{2}{3} t=\frac{1}{2}$$

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

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3} x=\frac{\sqrt{2}}{2} x=-\frac{\sqrt{2}}{2}$$