Question 173540


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



{{{(x-2)^2=(3)/(5)}}} Divide both sides by {{{5}}}.



{{{x-2=0+-sqrt(3/5)}}} Take the square root of both sides.



{{{x-2=sqrt(3/5)}}} or {{{x-2=-sqrt(3/5)}}} Break up the "plus/minus" to form two equations.



{{{x-2=sqrt(15)/5}}} or {{{x-2=-sqrt(15)/5}}}  Simplify the square root.



{{{x=2+sqrt(15)/5}}} or {{{x=2-sqrt(15)/5}}} Add {{{2}}} to both sides.



{{{x=(10+sqrt(15))/(5)}}} or {{{x=(10-sqrt(15))/(5)}}} Combine the fractions.



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Answer:



So the solutions are {{{x=(10+sqrt(15))/(5)}}} or {{{x=(10-sqrt(15))/(5)}}}.