Solve -x^4+2x^2-3/4=0

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

Solve for x

$$x = -\frac{\sqrt{6}}{2} \approx -1.224744871$$

$$x = \frac{\sqrt{6}}{2} \approx 1.224744871$$

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

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-t^{2}+2t-\frac{3}{4}=0$$

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 -1 for a, 2 for b, and -\frac{3}{4} for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\left(-1\right)\left(-\frac{3}{4}\right)}}{-2}$$

Do the calculations.

$$t=\frac{-2±1}{-2}$$

Solve the equation t=\frac{-2±1}{-2} when ± is plus and when ± is minus.

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

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

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