Solve 3x^4=7x^2-2

$$3 x ^ { 4 } = 7 x ^ { 2 } - 2$$

Solve for x

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

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

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps Using the Quadratic Formula

Subtract 7x^{2} from both sides.

$$3x^{4}-7x^{2}=-2$$

Add 2 to both sides.

$$3x^{4}-7x^{2}+2=0$$

Substitute t for x^{2}.

$$3t^{2}-7t+2=0$$

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

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 3\times 2}}{2\times 3}$$

Do the calculations.

$$t=\frac{7±5}{6}$$

Solve the equation t=\frac{7±5}{6} when ± is plus and when ± is minus.

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

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

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