Question 250467


{{{(4x-2)^2=8}}} Start with the given equation.



{{{4x-2=""+-sqrt(8)}}} Take the square root of both sides.



{{{4x-2=sqrt(8)}}} or {{{4x-2=-sqrt(8)}}} Break up the "plus/minus" to form two equations.



{{{4x-2=2*sqrt(2)}}} or {{{4x-2=-2*sqrt(2)}}}  Simplify the square root.



{{{4x=2+2*sqrt(2)}}} or {{{4x=2-2*sqrt(2)}}} Add {{{2}}} to both sides.



{{{x=(2+2*sqrt(2))/4}}} or {{{x=(2-2*sqrt(2))/4}}} Divide both sides by 4.



{{{x=(1+sqrt(2))/2}}} or {{{x=(1-sqrt(2))/2}}} Reduce.



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Answer:



So the solutions are {{{x=(1+sqrt(2))/2}}} or {{{x=(1-sqrt(2))/2}}}.