Question 114778
I'm going to assume you mean {{{sqrt(x+7)+5=x}}}.


1) Add -5 to both sides
{{{sqrt(x+7)=x-5}}}


2) Square both sides
{{{x+7=x^2-10x+25}}}


3) Collect terms and put in standard form
{{{x^2-11x+18=0}}}


4) Factor 
{{{-9*-2=18}}}
{{{-9+(-2)=-11}}}
{{{(x-9)(x-2)=0}}}
{{{x=9}}} or {{{x=2}}}


Check:
{{{sqrt(9+7)+5=9}}}
{{{sqrt(16)+5=9}}}
{{{4+5=9}}} Check

{{{sqrt(2+7)+5=2}}}
{{{sqrt(9)+5=2}}}
{{{3+5<>2}}} Does not check. Why?  By squaring both sides of the equation in step 2), you introduced an extraneous root that is invalid in the original equation.  Therefore exclude {{{x=2}}} from the solution set.  The only correct solution is {{{x=9}}}


Graphically:

{{{graph(400, 400, -8, 25, -10, 14, sqrt(x+7)+5-x)}}}