Solve (x-3)^2+1=0

$$( x - 3 ) ^ { 2 } + 1 = 0$$

Solve for x (complex solution)

$$x=3-i$$

$$x=3+i$$

Steps by Finding Square Root

Subtracting 1 from itself leaves 0.

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

Take the square root of both sides of the equation.

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

Add 3 to both sides of the equation.

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

Subtracting -3 from itself leaves 0.

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

Subtract -3 from i.

$$x=3+i$$

Subtract -3 from -i.

$$x=3-i$$

The equation is now solved.

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