How do you solve the quadratic equation by completing the square: #x^2 – 8x + 12 = 0#?

2 Answers
Jul 13, 2015

Answer:

Work out which factors of 12 add together to give 8. You can then factorise the equation. 12 is either #3*4# or #6*2# - #3+4 = 7# so that won't work, but #6 + 2 = 8# so that does work.

Explanation:

#(x - 6)(x-2) = 0#

Jul 13, 2015

Answer:

#x=6# or #x=2#
#color(white)("XXXX")#(solved by completion of squares method)

Explanation:

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#