Solve 2x^4+2x^2-24=0

$$2 x ^ { 4 } + 2 x ^ { 2 } - 24 = 0$$

Solve for x (complex solution)

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

$$x=-2i$$

$$x=2i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$2t^{2}+2t-24=0$$

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, 2 for b, and -24 for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{-2±14}{4}$$

Solve the equation t=\frac{-2±14}{4} when ± is plus and when ± is minus.

$$t=3 t=-4$$

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

$$x=-\sqrt{3} x=\sqrt{3} x=-2i x=2i$$

Solve for x

$$x=-\sqrt{3}\approx -1.732050808$$

$$x=\sqrt{3}\approx 1.732050808$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$2t^{2}+2t-24=0$$

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, 2 for b, and -24 for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{-2±14}{4}$$

Solve the equation t=\frac{-2±14}{4} when ± is plus and when ± is minus.

$$t=3 t=-4$$

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

$$x=\sqrt{3} x=-\sqrt{3}$$