If #3x^2-2x+7=0#, what is #(x-1/3)^2#?

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Answer 1 · 2016-07-30T23:32:35

not sure what you're needing here

is this a substitution question?

Answer 2 · 2016-07-30T23:37:25

#(x-1/3)^2 = -20/9#

#0 = 3x^2-2x+7#

#= 3(x^2-2/3+7/3)#

#= 3((x-1/3)^2-1/9+7/3)#

#= 3((x-1/3)^2+20/9)#

Hence #(x-1/3)^2 = -20/9#

So #x-1/3 = +-sqrt(-20/9) = +-(2sqrt(5))/3i#

So #x=1/3+-(2sqrt(5))/3i#