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

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

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

Divide both sides by 4. Zero divided by any non-zero number gives zero.

$$\left(x^{2}+2\right)^{2}=0$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+2\right)^{2}.

$$\left(x^{2}\right)^{2}+4x^{2}+4=0$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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.

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