Question 140623
{{{(3x-1)^2=12}}} Start with the given equation



{{{3x-1=0+-sqrt(12)}}} Take the square root of both sides



Break up the expression and simplify


{{{3x-1=2*sqrt(3)}}} or {{{3x-1=-2*sqrt(3)}}}



Add 1 to both sides in each case


{{{3x=2*sqrt(3)+1}}} or {{{3x=-2*sqrt(3)+1}}}



Divide both sides by 3 to isolate x in each case


{{{x=(2*sqrt(3)+1)/3}}} or {{{x=(-2*sqrt(3)+1)/3}}}



Rearrange the terms (this step is not necessary, but you're most likely to see the answer in this format)



{{{x=(1+2*sqrt(3))/3}}} or {{{x=(1-2*sqrt(3))/3}}}




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Answer:


So the solution set is exactly


{{{x=(1+2*sqrt(3))/3}}} or {{{x=(1-2*sqrt(3))/3}}}


which is approximately


{{{x=1.48803}}} or {{{x=-.82137}}}