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

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

Solve for x (complex solution)

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

$$x=\sqrt{2}i\approx 1.414213562i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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 4 for c in the quadratic formula.

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

Do the calculations.

$$t=\frac{-4±0}{2}$$

Solutions are the same.

$$t=-2$$

Since x=t^{2}, the solutions are obtained by solving the equation for each t.

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