# How do you solve #X^2-2x=-2#?

##### 2 Answers

There are no Real solutions to this equation.

If Complex solutions are permitted:

#### Explanation:

Given

Complete the square

#color(white)("XXX")x^2-2x+1 = -2+1

Re-write as a squared binomial and simplify the right side:

#color(white)("XXX")(x-1)^2 = -1

At this point we can see that there are no Real solutions (since any Real value squared is

If we allow Complex solutions:

And adding

There are no Real solutions to this equation.

If Complex solutions are permitted:

#### Explanation:

Given

Complete the square

#color(white)("XXX")x^2-2x+1 = -2+1

Re-write as a squared binomial and simplify the right side:

#color(white)("XXX")(x-1)^2 = -1

At this point we can see that there are no Real solutions (since any Real value squared is

If we allow Complex solutions:

And adding