Solve 0=2x^4-5x^2-7

$$0 = 2 { x }^{ 4 } -5 { x }^{ 2 } -7$$

Solve for x (complex solution)

$$x = \frac{\sqrt{14}}{2} \approx 1.870828693$$

$$x = -\frac{\sqrt{14}}{2} \approx -1.870828693$$

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

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

$$2x^{4}-5x^{2}-7=0$$

Substitute t for x^{2}.

$$2t^{2}-5t-7=0$$

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, -5 for b, and -7 for c in the quadratic formula.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 2\left(-7\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{5±9}{4}$$

Solve the equation t=\frac{5±9}{4} when ± is plus and when ± is minus.

$$t=\frac{7}{2} t=-1$$

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

$$x=-\frac{\sqrt{14}}{2} x=\frac{\sqrt{14}}{2} x=-i x=i$$

Solve for x

$$x = -\frac{\sqrt{14}}{2} \approx -1.870828693$$

$$x = \frac{\sqrt{14}}{2} \approx 1.870828693$$

Steps Using the Quadratic Formula

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

$$2x^{4}-5x^{2}-7=0$$

Substitute t for x^{2}.

$$2t^{2}-5t-7=0$$

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, -5 for b, and -7 for c in the quadratic formula.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 2\left(-7\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{5±9}{4}$$

Solve the equation t=\frac{5±9}{4} when ± is plus and when ± is minus.

$$t=\frac{7}{2} t=-1$$

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

$$x=\frac{\sqrt{14}}{2} x=-\frac{\sqrt{14}}{2}$$