How do you solve by completing the square: #x^2 - 4x +2 = 0#?

1 Answer
Alan P.
Apr 3, 2015

(Please note that I edited your question to place a plus sign between the #4x# and the #2#; if you meant something else, perhaps a minus sign, please re-post).

#x^2-4x+2=0#

Subtract the constant (#2#) from both sides
#x^2-4x=-2#

If #x^2 +4x# are the first two terms of a square of the form #(x+a)^2#
then
#a=-2# and the term needed to complete the square is #a^2 =4#

Add 4 to both sides of the equation
#x^2-4x+4 = 4-2#

Rewrite the left side as a square
#(x-2)^2 = 2#

Take the square root of both sides
#x-2 = +-sqrt(2)#

Giving the solutions
#x = 2+-sqrt(2)#

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