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

2 Answers
Alan P.
Oct 1, 2015

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

Alan P.
Oct 1, 2015

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

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