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

1 Answer
Jun 12, 2015

Answer:

#x=1+i#

#x=1-i#

Explanation:

Make a perfect square trinomial by completing the square. A perfect square trinomial has the form of #a^2+2ab+b^2=(a+b)^2# or #a^2-2ab+b^2=(a-b)^2#.

#x^2-2x+2=0#

Subtract #2# from both sides of the equation.

#x^2-2x=-2#

Divide the coefficient of the #x# term by #2# and square the result. Add it to both sides of the equation.

#(-2)/2=-1#; #-1^2=1#

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

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

There is now a perfect square trinomial on the left side of the equation.

Factor the trinomial.

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

Take the square root of both sides and solve for #x#.

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

#x-1=+-i#

#x=1+-i#