Solve 2(x-1)^2=-32

$$2 ( x - 1 ) ^ { 2 } = - 32$$

Solve for x (complex solution)

$$x=1-4i$$

$$x=1+4i$$

Steps by Finding Square Root

Dividing by 2 undoes the multiplication by 2.

$$\left(x-1\right)^{2}=-\frac{32}{2}$$

Divide -32 by 2.

$$\left(x-1\right)^{2}=-16$$

Take the square root of both sides of the equation.

$$x-1=4i x-1=-4i$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=4i-\left(-1\right) x-1-\left(-1\right)=-4i-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=4i-\left(-1\right) x=-4i-\left(-1\right)$$

Subtract -1 from 4i.

$$x=1+4i$$

Subtract -1 from -4i.

$$x=1-4i$$

The equation is now solved.

$$x=1+4i x=1-4i$$