Question 823332
{{{(3x-1)^2=5}}} Start with the given equation.



{{{3x-1=""+-sqrt(5)}}} Take the square root of both sides.



{{{3x-1=sqrt(5)}}} or {{{3x-1=-sqrt(5)}}} Break up the "plus/minus" to form two equations.



{{{3x-1=sqrt(5)}}} or {{{3x-1=-sqrt(5)}}}  Simplify the square root.



{{{3x=1+sqrt(5)}}} or {{{3x=1-sqrt(5)}}} Add {{{1}}} to both sides.



{{{x=(1+sqrt(5))/3}}} or {{{x=(1-sqrt(5))/3}}} Divide both sides by 3.



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Answer:



So the solutions are {{{x=(1+sqrt(5))/3}}} or {{{x=(1-sqrt(5))/3}}}.