Solve 2(x-3)^2=-32?

$$2 ( x - 3 ) ^ { 2 } = - 32 ?$$

Solve for x (complex solution)

$$x=3-4i$$

$$x=3+4i$$

Steps by Finding Square Root

Dividing by 2 undoes the multiplication by 2.

$$\left(x-3\right)^{2}=-\frac{32}{2}$$

Divide -32 by 2.

$$\left(x-3\right)^{2}=-16$$

Take the square root of both sides of the equation.

$$x-3=4i x-3=-4i$$

Add 3 to both sides of the equation.

$$x-3-\left(-3\right)=4i-\left(-3\right) x-3-\left(-3\right)=-4i-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$x=4i-\left(-3\right) x=-4i-\left(-3\right)$$

Subtract -3 from 4i.

$$x=3+4i$$

Subtract -3 from -4i.

$$x=3-4i$$

The equation is now solved.

$$x=3+4i x=3-4i$$