Solve (x-1)^2+8=0

$$( x - 1 ) ^ { 2 } + 8 = 0$$

Solve for x (complex solution)

$$x=-2\sqrt{2}i+1\approx 1-2.828427125i$$

$$x=1+2\sqrt{2}i\approx 1+2.828427125i$$

Steps by Finding Square Root

Subtracting 8 from itself leaves 0.

$$\left(x-1\right)^{2}=-8$$

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

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

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

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

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

The equation is now solved.

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