Solve 3(x+5)^2=-2

$$3 ( x + 5 ) ^ { 2 } = - 2$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{3}-5\approx -5-0.816496581i$$

$$x=\frac{\sqrt{6}i}{3}-5\approx -5+0.816496581i$$

Steps by Finding Square Root

Dividing by 3 undoes the multiplication by 3.

$$\left(x+5\right)^{2}=-\frac{2}{3}$$

Take the square root of both sides of the equation.

$$x+5=\frac{\sqrt{6}i}{3} x+5=-\frac{\sqrt{6}i}{3}$$

Subtract 5 from both sides of the equation.

$$x+5-5=\frac{\sqrt{6}i}{3}-5 x+5-5=-\frac{\sqrt{6}i}{3}-5$$

Subtracting 5 from itself leaves 0.

$$x=\frac{\sqrt{6}i}{3}-5 x=-\frac{\sqrt{6}i}{3}-5$$