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

2 Answers
Oct 1, 2015

Answer:

There are no Real solutions to this equation.
If Complex solutions are permitted: #x=1+-i#

Explanation:

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

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 #> -1#)

If we allow Complex solutions:
#color(white)("XXX")x-1 = +-sqrt(-1) = +-i#

And adding #1# to both sides:
#color(white)("XXX")x= 1+-i#

Oct 1, 2015

Answer:

There are no Real solutions to this equation.
If Complex solutions are permitted: #x=1+-i#

Explanation:

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

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 #> -1#)

If we allow Complex solutions:
#color(white)("XXX")x-1 = +-sqrt(-1) = +-i#

And adding #1# to both sides:
#color(white)("XXX")x= 1+-i#