Question 894222
{{{sqrt(38x+647) +17= x+35 }}}
{{{sqrt(38x+647)=x+18}}}
{{{38x+647=(x+18)^2}}}
{{{38x+647=x^2+36x+324}}}
{{{x^2-2x-323=0}}}
{{{(x-19)(x+17)=0}}}
Two solutions:
{{{x-19=0}}}
{{{x=19}}}
and
{{{x+17=0}}}
{{{x=-17}}}
Now go back to the original equation and plug in the values and make 
sure neither of the solutions are extraneous solutions (don't solve the equation).