Question 110344
Solve by using the Square Root Property 
 {{{(x-5)^2=7}}}

If we have

        {{{x^2  =  k }}}

then we can {{{take}}}{{{ the }}}{{{square}}}{{{ root}}} of {{{both}}}{{{ sides}}} to solve for{{{ x}}}.
	
For any positive number {{{k}}},
if          
          {{{x^2 = k }}}
then         
          {{{x   = sqrt(k)}}}     or    {{{ x  =  - sqrt(k)}}}    

so, we will have:

 {{{(x-5)^2=7}}}

 {{{sqrt((x-5)^2)=sqrt(7)}}}

 {{{x-5=sqrt(7)}}}........move {{{-5}}} to the right

 {{{x = 5 + sqrt(7)}}}...................{{{sqrt(7)= 2.65}}}

{{{x = 5 + 2.65}}}

{{{x = 7.65}}}