document.write( "Question 702144: Find all solutions of\r
\n" ); document.write( "\n" ); document.write( "sqrt(x+10)-(6/sqrt(x+10)=5 \n" ); document.write( "

Algebra.Com's Answer #432838 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%28x%2B10%29-6%2Fsqrt%28x%2B10%29=5\"$ is asking for a change of variable with $\"y=sqrt%28x%2B10%29\"$
\n" ); document.write( "The equation transforms into
\n" ); document.write( " $\"y-6%2Fy=5\"$
\n" ); document.write( "Multiplying both sides of the equation time $\"y\"$ ,
\n" ); document.write( "we do not lose any solution.
\n" ); document.write( "Any solution we gain can be eliminated later.
\n" ); document.write( "Multiplying both sides of the equation time $\"y\"$ we get
\n" ); document.write( " $\"y%5E2-6=5y\"$ --> $\"y%5E2-5y-6=0\"$
\n" ); document.write( "Factoring, we get $\"%28y-6%29%28y%2B1%29=0\"$
\n" ); document.write( "The solutions to that equation are $\"y=-1\"$ and $\"y=6\"$ .
\n" ); document.write( "They are both solutions of $\"y-6%2Fy=5\"$ ,
\n" ); document.write( "but $\"y=sqrt%28x%2B10%29\"$ is by definition a positive number,
\n" ); document.write( "so we eliminate $\"y=-1\"$ as a solution.
\n" ); document.write( "We continue with $\"sqrt%28x%2B10%29=6\"$ --> $\"x%2B10=6%5E2\"$ --> $\"x%2B10=36\"$
\n" ); document.write( " $\"x%2B10=36\"$ --> $\"x=36-10\"$ --> $\"highlight%28x=26%29\"$ \n" ); document.write( "

\n" );