Solve x^4+2x^2-48=0

$$x ^ { 4 } + 2 x ^ { 2 } - 48 = 0$$

Solve for x (complex solution)

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

$$x=-2\sqrt{2}i\approx -0-2.828427125i$$

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+2t-48=0$$

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, 2 for b, and -48 for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\times 1\left(-48\right)}}{2}$$

Do the calculations.

$$t=\frac{-2±14}{2}$$

Solve the equation t=\frac{-2±14}{2} when ± is plus and when ± is minus.

$$t=6 t=-8$$

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

$$x=-\sqrt{6} x=\sqrt{6} x=-2\sqrt{2}i x=2\sqrt{2}i$$

Solve for x

$$x=-\sqrt{6}\approx -2.449489743$$

$$x=\sqrt{6}\approx 2.449489743$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+2t-48=0$$

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, 2 for b, and -48 for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\times 1\left(-48\right)}}{2}$$

Do the calculations.

$$t=\frac{-2±14}{2}$$

Solve the equation t=\frac{-2±14}{2} when ± is plus and when ± is minus.

$$t=6 t=-8$$

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

$$x=\sqrt{6} x=-\sqrt{6}$$