How do you solve using the completing the square method #x^2-2x+2#?

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Answer 1 · 2016-04-27T17:15:46

The solutions are:
#color(green)(x = sqrt (-1) + 1 # or, # color(green)(x = -sqrt (-1) + 1#

#x^2 - 2x + 2#

#x^2 -2x = -2#

To write the Left Hand Side as a Perfect Square, we add 1 to both sides:

#x^2 -2x +1 = -2 + 1#

#x^2 - 2 * 1 * x + 1^2 = -1#

Using the Identity #color(blue)((a-b)^2 = a^2 - 2ab + b^2#, we get

#(x - 1)^2 = -1 #

#x - 1 = sqrt(-1)# or #x - 1 = -sqrt(-1)#

#color(green)(x = sqrt (-1) + 1 # or # color(green)(x = -sqrt (-1) + 1#