Solve -left(x-1right)^2-12=0

$$- { \left(x-1 \right) }^{ 2 } -12=0$$

Solve for x (complex solution)

$$x=-2\sqrt{3}i+1\approx 1-3.464101615i$$

$$x=1+2\sqrt{3}i\approx 1+3.464101615i$$

Steps by Finding Square Root

Subtracting 12 from itself leaves 0.

$$-\left(x-1\right)^{2}=12$$

Divide both sides by -1.

$$\frac{-\left(x-1\right)^{2}}{-1}=\frac{12}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\left(x-1\right)^{2}=\frac{12}{-1}$$

Divide 12 by -1.

$$\left(x-1\right)^{2}=-12$$

Take the square root of both sides of the equation.

$$x-1=2\sqrt{3}i x-1=-2\sqrt{3}i$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=2\sqrt{3}i-\left(-1\right) x-1-\left(-1\right)=-2\sqrt{3}i-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=2\sqrt{3}i-\left(-1\right) x=-2\sqrt{3}i-\left(-1\right)$$

Subtract -1 from 2i\sqrt{3}.

$$x=1+2\sqrt{3}i$$

Subtract -1 from -2i\sqrt{3}.

$$x=-2\sqrt{3}i+1$$

The equation is now solved.

$$x=1+2\sqrt{3}i x=-2\sqrt{3}i+1$$