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

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{2}-1\approx -1-1.224744871i$$

$$x=\frac{\sqrt{6}i}{2}-1\approx -1+1.224744871i$$

Steps by Finding Square Root

Subtracting 3 from itself leaves 0.

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

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

Divide 3 by -2.

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

Take the square root of both sides of the equation.

$$x+1=\frac{\sqrt{6}i}{2} x+1=-\frac{\sqrt{6}i}{2}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{\sqrt{6}i}{2}-1 x+1-1=-\frac{\sqrt{6}i}{2}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{\sqrt{6}i}{2}-1 x=-\frac{\sqrt{6}i}{2}-1$$