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

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

Solve for x (complex solution)

$$x=-\sqrt{2}i+1\approx 1-1.414213562i$$

$$x=1+\sqrt{2}i\approx 1+1.414213562i$$

Steps by Finding Square Root

Subtracting 2 from itself leaves 0.

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

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

Subtract -1 from i\sqrt{2}.

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

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

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

The equation is now solved.

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