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

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

Solve for x (complex solution)

$$x=2$$

$$x=-2$$

$$x=-\sqrt{6}i\approx -0-2.449489743i$$

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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

$$t=\frac{-2±\sqrt{2^{2}-4\times 1\left(-24\right)}}{2}$$

Do the calculations.

$$t=\frac{-2±10}{2}$$

Solve the equation t=\frac{-2±10}{2} when ± is plus and when ± is minus.

$$t=4 t=-6$$

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

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

Solve for x

$$x=-2$$

$$x=2$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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

$$t=\frac{-2±\sqrt{2^{2}-4\times 1\left(-24\right)}}{2}$$

Do the calculations.

$$t=\frac{-2±10}{2}$$

Solve the equation t=\frac{-2±10}{2} when ± is plus and when ± is minus.

$$t=4 t=-6$$

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

$$x=2 x=-2$$