How do you solve using the completing the square method #9(x^2) - 18x = -3#?

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Answer 1 · 2018-04-10T18:41:44

You need to use the formula: #(a-b)^2=a^2-2ab+b^2#

If we manipulate the equation given to get #9x^2-18x+3=0#, using the formula above we can see that:

#9x^2=a^2#, and that #-18x=-2ab#

So from the first we have #3x=a# and substituting this in the second we have

#-6 * 3x=-6a=-2ab#, and then

#-6=-2b# and from here #b=3#

Now completing the square in the equation given :

#9x^2-18x+3=9x^2-18x+9-6=0=(3x-3)^2-6=0#

that is:

#(3x-3)^2=6#, and we have two solutions:

#(3x-3)=+sqrt6#
#(3x-3)=-sqrt6#, and then:
#x=(3+sqrt6)/3# and
#x=(3-sqrt6)/3#