Step 1: Keep all terms containing $ x $ on one side. Move $ 2 $ to the right.
$$ x^2-2x = -2 $$Step 2: Take half of the x -term coefficient and square it. Add this value to both sides.
The x-term coefficient = $ -2 $
The half of the x-term coefficient = $ -1 $
After squaring we have $ (-1)^2 = 1 $
When we add $ 1 $ to both sides we have:
$$ x^2-2x+1 = -2 + 1 $$Step 3: Simplify right side.
$$ x^2-2x+1 = -1 $$Step 4: Write the perfect square on the left.
$$ \left(x + 1 \right)^2 = -1 $$Step 5: Take the square root of both sides.
$$ x + 1 = \pm \sqrt { -1 } $$Step 6: Solve for $ x $.
$ x_1,x_2 = - 1 \pm \sqrt{ -1 } $
that is,
$ x_1 = 1+i $
$ x_2 = 1-i $