Solve 2x^4-15x^2-8=0

$$2 { x }^{ 4 } -15 { x }^{ 2 } -8 = 0$$

Solve for x (complex solution)

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

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

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$2t^{2}-15t-8=0$$

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, -15 for b, and -8 for c in the quadratic formula.

$$t=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{15±17}{4}$$

Solve the equation t=\frac{15±17}{4} when ± is plus and when ± is minus.

$$t=8 t=-\frac{1}{2}$$

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

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

Solve for x

$$x=-2\sqrt{2}\approx -2.828427125$$

$$x=2\sqrt{2}\approx 2.828427125$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$2t^{2}-15t-8=0$$

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, -15 for b, and -8 for c in the quadratic formula.

$$t=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{15±17}{4}$$

Solve the equation t=\frac{15±17}{4} when ± is plus and when ± is minus.

$$t=8 t=-\frac{1}{2}$$

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

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