Question 89112
{{{(x-4)^2=25}}}


{{{x-4=sqrt(25)}}} Take the square root of both sides


*[Tex \LARGE x-4=\pm5] Take the square root of 25


So the expression breaks down to 

{{{x-4=5}}} or {{{x-4=-5}}}


Lets look at the first equation {{{x-4=5}}}

{{{x=4+5}}} Add 4 to both sides


{{{x=9}}} Combine like terms



Now lets look at the first equation {{{x-4=-5}}}

{{{x=4-5}}} Add 4 to both sides


{{{x=-1}}} Combine like terms

So we get 2 answers {{{x=-1}}} and {{{x=9}}}



Check:

{{{(-1-4)^2=25}}} plug in x=-1


{{{(-5)^2=25}}}


{{{25=25}}} works



{{{(9-4)^2=25}}} plug in x=9


{{{(5)^2=25}}}


{{{25=25}}} works