Solve -2x^4+9x^2+5=0

$$- 2 x ^ { 4 } + 9 x ^ { 2 } + 5 = 0$$

Solve for x (complex solution)

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

$$x=-\frac{\sqrt{2}i}{2}\approx -0-0.707106781i$$

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=\sqrt{5}\approx 2.236067977$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-2t^{2}+9t+5=0$$

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 -2 for a, 9 for b, and 5 for c in the quadratic formula.

$$t=\frac{-9±\sqrt{9^{2}-4\left(-2\right)\times 5}}{-2\times 2}$$

Do the calculations.

$$t=\frac{-9±11}{-4}$$

Solve the equation t=\frac{-9±11}{-4} when ± is plus and when ± is minus.

$$t=-\frac{1}{2} t=5$$

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

$$x=-\frac{\sqrt{2}i}{2} x=\frac{\sqrt{2}i}{2} x=-\sqrt{5} x=\sqrt{5}$$

Solve for x

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=\sqrt{5}\approx 2.236067977$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-2t^{2}+9t+5=0$$

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 -2 for a, 9 for b, and 5 for c in the quadratic formula.

$$t=\frac{-9±\sqrt{9^{2}-4\left(-2\right)\times 5}}{-2\times 2}$$

Do the calculations.

$$t=\frac{-9±11}{-4}$$

Solve the equation t=\frac{-9±11}{-4} when ± is plus and when ± is minus.

$$t=-\frac{1}{2} t=5$$

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

$$x=\sqrt{5} x=-\sqrt{5}$$