Question 741133
Square both sides of the equation... TWICE.


{{{sqrt(x + 73) + sqrt(x - 8) = 9}}}
{{{sqrt(x+73)=9-sqrt(x-8)}}}
{{{x+73=81-2*9*sqrt(x-8)+x-8}}}
{{{73=81-8-18*sqrt(x-8)}}}
{{{73=73-18*sqrt(x-8)}}}
{{{-18*sqrt(x-8)=0}}}
{{{sqrt(x-8)=0}}}

This so far seems to be simpler than some of these can be, so squaring again might be unnecessary.

{{{x-8=0}}}
{{{highlight(x=8)}}}.