Question 214781

{{{(12x-8)^2=54}}} Start with the given equation.



{{{12x-8=""+-sqrt(54)}}} Take the square root of both sides.



{{{12x-8=sqrt(54)}}} or {{{12x-8=-sqrt(54)}}} Break up the "plus/minus" to form two equations.



{{{12x-8=3*sqrt(6)}}} or {{{12x-8=-3*sqrt(6)}}}  Simplify the square root.



{{{12x=8+3*sqrt(6)}}} or {{{12x=8-3*sqrt(6)}}} Add {{{8}}} to both sides.



{{{x=(8+3*sqrt(6))/12}}} or {{{x=(8-3*sqrt(6))/12}}} Divide both sides by 12 to isolate 'x'.


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Answer:



So the solutions are {{{x=(8+3*sqrt(6))/12}}} or {{{x=(8-3*sqrt(6))/12}}} .