Question 891420
You want to square this on both sides, TWICE.  Some adjustments between the first and second squaring is needed.

First Squaring
{{{sqrt(x)+sqrt(x+7)=7}}}
{{{x+2sqrt(x)sqrt(x+7)+x+7=49}}}
{{{2sqrt(x)sqrt(x+7)=49-2x-7}}}
{{{2sqrt(x)sqrt(x+7)=42-2x}}}
{{{sqrt(x)sqrt(x+7)=21-x}}}
Second Squaring
{{{x*(x+7)=(21-x)^2}}}
{{{x^2+7x=441-42x+x^2}}}
{{{7x=441-42x}}}
{{{7x+42x=441}}}
{{{49x=441}}}
{{{x=441/49}}}
{{{x=(21*21)/(7*7)}}}
{{{highlight(x=9)}}}