Solve -x^4+18x^2-16=0

$$- x ^ { 4 } + 18 x ^ { 2 } - 16 = 0$$

Solve for x

$$x=\frac{\sqrt{10}-\sqrt{26}}{2}\approx -0.968370927$$

$$x=\frac{\sqrt{26}-\sqrt{10}}{2}\approx 0.968370927$$

$$x = \frac{\sqrt{10} + \sqrt{26}}{2} \approx 4.130648587$$

$$x=\frac{-\sqrt{10}-\sqrt{26}}{2}\approx -4.130648587$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-t^{2}+18t-16=0$$

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, 18 for b, and -16 for c in the quadratic formula.

$$t=\frac{-18±\sqrt{18^{2}-4\left(-1\right)\left(-16\right)}}{-2}$$

Do the calculations.

$$t=\frac{-18±2\sqrt{65}}{-2}$$

Solve the equation t=\frac{-18±2\sqrt{65}}{-2} when ± is plus and when ± is minus.

$$t=9-\sqrt{65} t=\sqrt{65}+9$$

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

$$x=-\frac{\sqrt{10}-\sqrt{26}}{2} x=\frac{\sqrt{10}-\sqrt{26}}{2} x=\frac{\sqrt{10}+\sqrt{26}}{2} x=-\frac{\sqrt{10}+\sqrt{26}}{2}$$