Solve (x-6)^2+4=1

$$( x - 6 ) ^ { 2 } + 4 = 1$$

Solve for x (complex solution)

$$x=-\sqrt{3}i+6\approx 6-1.732050808i$$

$$x=6+\sqrt{3}i\approx 6+1.732050808i$$

Steps by Finding Square Root

Subtracting 4 from itself leaves 0.

$$\left(x-6\right)^{2}=1-4$$

Subtract 4 from 1.

$$\left(x-6\right)^{2}=-3$$

Take the square root of both sides of the equation.

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

Add 6 to both sides of the equation.

$$x-6-\left(-6\right)=\sqrt{3}i-\left(-6\right) x-6-\left(-6\right)=-\sqrt{3}i-\left(-6\right)$$

Subtracting -6 from itself leaves 0.

$$x=\sqrt{3}i-\left(-6\right) x=-\sqrt{3}i-\left(-6\right)$$

Subtract -6 from i\sqrt{3}.

$$x=6+\sqrt{3}i$$

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

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

The equation is now solved.

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