Question 1054083
Two irrational expression, power of one-half, each; squaring done two times.  Watch for either solution being incorrect for the original equation.


{{{sqrt(x+6)=3-sqrt(x)}}}
{{{x+6=9-6*sqrt(x)+x}}}
{{{0=3-6sqrt(x)}}}
{{{6*sqrt(x)=3}}}
{{{sqrt(x)=1/2}}}
{{{x=1/4}}}-------------seems to be only this solution; none others occur.


Check if you want to be sure.
{{{sqrt(1/4+6)+sqrt(1/4)=what}}}
{{{sqrt(25/4)+1/2}}}
{{{5/2+1/2}}}
{{{6/2=3}}}
Check works.