How do you solve #5x^2-30x+5=0# by completing the square?

1 Answer
Shwetank Mauria
Aug 4, 2016

#x=3-2sqrt2# or #x=3+2sqrt2#

Explanation:

To solve #5x^2-30x+5=0#, let us first divide both sides by #5# whic gives us

#x^2-6x+1=0#

Now to complete square for #x^2-6x#, recalling identity #(x-a)^2=x^2-2ax+a^2#, we must add and subtract square of half of the coefficient of #x# i.e. #(6/2)^2=9#, hence we have

#x^2-6x+9-9+1=0# or

#(x-3)^2-8=0# or #(x-3)^2-(2sqrt2)^2=0# which can be factorized as

#(x-3+2sqrt2)(x-3-2sqrt2)=0#

Hence #x=3-2sqrt2# or #x=3+2sqrt2#

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