Solve x^4+4x^2=-3

$$x ^ { 4 } + 4 x ^ { 2 } = - 3$$

Solve for x (complex solution)

$$x=i$$

$$x=-i$$

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

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

Steps Using the Quadratic Formula

Add 3 to both sides.

$$x^{4}+4x^{2}+3=0$$

Substitute t for x^{2}.

$$t^{2}+4t+3=0$$

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, 4 for b, and 3 for c in the quadratic formula.

$$t=\frac{-4±\sqrt{4^{2}-4\times 1\times 3}}{2}$$

Do the calculations.

$$t=\frac{-4±2}{2}$$

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

$$t=-1 t=-3$$

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

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