How do you solve the quadratic equation by completing the square: #x^2-6x=0#?

1 Answer
Jul 13, 2015

Answer:

#x^2-6 = 0#
#rArr x=0# or #x=6#
#color(white)("XXXX")#(by completing the square)

Explanation:

Given #x^2 - 6x = 0#

#color(white)("XXXX")#If #x^2# and #-6x# 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 (since #-2ax = -6ax#) #rArr a = 3#

#color(white)("XXXX")#and the third term must be #a^2 = 9#

#color(white)("XXXX")#So we need to add #9# (to both sides) to "complete the square"
#x^2-6x+9 = 9#

#color(white)("XXXX")#Rewriting as a squared binomial
#(x-3)^2 = 9#

#color(white)("XXXX")#Taking the square root of both sides
#x-3 = +-sqrt(9) = +-3#

#color(white)("XXXX")#Adding 3 to both sides
#x = 6# or #x = 0#

(Note that, in this case, the solution would be simpler to determine by factoring).