Solve 0=-x^4+5x^2-4

$$0 = - x ^ { 4 } + 5 x ^ { 2 } - 4$$

Solve for x

$$x=-2$$

$$x=2$$

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$-x^{4}+5x^{2}-4=0$$

Substitute t for x^{2}.

$$-t^{2}+5t-4=0$$

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, 5 for b, and -4 for c in the quadratic formula.

$$t=\frac{-5±\sqrt{5^{2}-4\left(-1\right)\left(-4\right)}}{-2}$$

Do the calculations.

$$t=\frac{-5±3}{-2}$$

Solve the equation t=\frac{-5±3}{-2} when ± is plus and when ± is minus.

$$t=1 t=4$$

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

$$x=1 x=-1 x=2 x=-2$$