Solve 3(x+1)^2+2=0

$$3 ( x + 1 ) ^ { 2 } + 2 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{3}-1\approx -1-0.816496581i$$

$$x=\frac{\sqrt{6}i}{3}-1\approx -1+0.816496581i$$

Steps by Finding Square Root

Subtracting 2 from itself leaves 0.

$$3\left(x+1\right)^{2}=-2$$

Divide both sides by 3.

$$\frac{3\left(x+1\right)^{2}}{3}=-\frac{2}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(x+1\right)^{2}=-\frac{2}{3}$$

Take the square root of both sides of the equation.

$$x+1=\frac{\sqrt{6}i}{3} x+1=-\frac{\sqrt{6}i}{3}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{\sqrt{6}i}{3}-1 x+1-1=-\frac{\sqrt{6}i}{3}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{\sqrt{6}i}{3}-1 x=-\frac{\sqrt{6}i}{3}-1$$