Given #x^2–8x+12=0#

#color(white)("XXXX")#Move the constant to the right side

#x^2-8x = -12#

#color(white)("XXXX")#If #x^2# and #-8x# are the first two terms of a squared binomial:

#color(white)("XXXX")##color(white)("XXXX")##(x+a)^2 = x^2+2ax+a^2#

#color(white)("XXXX")#then the third term needs to be #(a^2) = (8/2)^2#

#x^2-8x+(8/2)^2 = -12 +(8/2)^2#

#x^2-8x+4^2 = -12 +16#

#color(white)("XXXX")#rewrite the left side as a squared binomial

#color(white)("XXXX")# and simplify the right side.

#(x-4)^2 = 4#

#color(white)("XXXX")#Take the square root of both sides

#x-4 = +-2#

#color(white)("XXXX")#Add 4 to both sides

#x=6#

or

#x=2#