Solve 3(w+3)^2=-72

$$3 ( w + 3 ) ^ { 2 } = - 72$$

Solve for w

$$w=-2\sqrt{6}i-3\approx -3-4.898979486i$$

$$w=-3+2\sqrt{6}i\approx -3+4.898979486i$$

Steps by Finding Square Root

Dividing by 3 undoes the multiplication by 3.

$$\left(w+3\right)^{2}=-\frac{72}{3}$$

Divide -72 by 3.

$$\left(w+3\right)^{2}=-24$$

Take the square root of both sides of the equation.

$$w+3=2\sqrt{6}i w+3=-2\sqrt{6}i$$

Subtract 3 from both sides of the equation.

$$w+3-3=2\sqrt{6}i-3 w+3-3=-2\sqrt{6}i-3$$

Subtracting 3 from itself leaves 0.

$$w=2\sqrt{6}i-3 w=-2\sqrt{6}i-3$$

Subtract 3 from 2i\sqrt{6}.

$$w=-3+2\sqrt{6}i$$

Subtract 3 from -2i\sqrt{6}.

$$w=-2\sqrt{6}i-3$$

The equation is now solved.

$$w=-3+2\sqrt{6}i w=-2\sqrt{6}i-3$$