Question 184673
<pre><font size = 4 color = "indigo"><b>
{{{sqrt(x) + sqrt(x-5) = 5}}} 

Solve equation & check for extraneous solutions

{{{sqrt(x) + sqrt(x-5) = 5}}} 

Isolate the more complicated radical:

{{{sqrt(x-5) = 5 - sqrt(x)}}}

Square both sides

{{{(sqrt(x-5))^2 = (5 - sqrt(x))^2}}}

The left side is just {{{x-5}}} because it just
has one term in the parentheses. But the right 
side has two terms, so to square it you must
write it down twice and multiply it by itself:

{{{x-5 = (5 - sqrt(x))(5-sqrt(x))}}}

Use FOIL on the right:

{{{x-5 = 25 - 5sqrt(x)-5sqrt(x)+(sqrt(x))^2 }}}

{{{x-5 = 25 - 10sqrt(x)+x }}}

Simplify the equation

{{{10sqrt(x)=30}}}

Divide through by 10 

{{{sqrt(x)=3}}}

Square both sides:

{{{(sqrt(x))^2 = 3^2}}}

{{{x=9}}}

Check:

{{{sqrt(x) + sqrt(x-5) = 5}}}
{{{sqrt(9) + sqrt(9-5) = 5}}}
{{{sqrt(9) + sqrt(4) = 5}}}
{{{3+2=5}}}
{{{5=5}}}

So the solution is {{{9}}}

Edwin</pre>