Question 457550


{{{(n-5)^2=32}}} Start with the given equation.



{{{x-5=""+-sqrt(32)}}} Take the square root of both sides.



{{{n-5=sqrt(32)}}} or {{{n-5=-sqrt(32)}}} Break up the "plus/minus" to form two equations.



{{{n-5=4*sqrt(2)}}} or {{{n-5=-4*sqrt(2)}}}  Simplify the square root.



{{{n=5+4*sqrt(2)}}} or {{{n=5-4*sqrt(2)}}} Add {{{5}}} to both sides.



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Answer:



So the solutions are {{{n=5+4*sqrt(2)}}} or {{{n=5-4*sqrt(2)}}}.