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

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

Solve for x (complex solution)

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

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

Steps by Finding Square Root

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

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

Divide -\frac{1}{3} by \frac{1}{2} by multiplying -\frac{1}{3} by the reciprocal of \frac{1}{2}.

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

Take the square root of both sides of the equation.

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

Subtract 3 from both sides of the equation.

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

Subtracting 3 from itself leaves 0.

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