document.write( "Question 184673This question is from textbook
\n" ); document.write( ": squareroot x + squareroot x-5 = 5\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solve equation & check for extraneous solutions
\n" ); document.write( "

Algebra.Com's Answer #138600 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"sqrt%28x%29+%2B+sqrt%28x-5%29+=+5\" \r\n" );
document.write( "\r\n" );
document.write( "Solve equation & check for extraneous solutions\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%28x%29+%2B+sqrt%28x-5%29+=+5\" \r\n" );
document.write( "\r\n" );
document.write( "Isolate the more complicated radical:\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%28x-5%29+=+5+-+sqrt%28x%29\"\r\n" );
document.write( "\r\n" );
document.write( "Square both sides\r\n" );
document.write( "\r\n" );
document.write( "\"%28sqrt%28x-5%29%29%5E2+=+%285+-+sqrt%28x%29%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "The left side is just \"x-5\" because it just\r\n" );
document.write( "has one term in the parentheses. But the right \r\n" );
document.write( "side has two terms, so to square it you must\r\n" );
document.write( "write it down twice and multiply it by itself:\r\n" );
document.write( "\r\n" );
document.write( "\"x-5+=+%285+-+sqrt%28x%29%29%285-sqrt%28x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use FOIL on the right:\r\n" );
document.write( "\r\n" );
document.write( "\"x-5+=+25+-+5sqrt%28x%29-5sqrt%28x%29%2B%28sqrt%28x%29%29%5E2+\"\r\n" );
document.write( "\r\n" );
document.write( "\"x-5+=+25+-+10sqrt%28x%29%2Bx+\"\r\n" );
document.write( "\r\n" );
document.write( "Simplify the equation\r\n" );
document.write( "\r\n" );
document.write( "\"10sqrt%28x%29=30\"\r\n" );
document.write( "\r\n" );
document.write( "Divide through by 10 \r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%28x%29=3\"\r\n" );
document.write( "\r\n" );
document.write( "Square both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"%28sqrt%28x%29%29%5E2+=+3%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=9\"\r\n" );
document.write( "\r\n" );
document.write( "Check:\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%28x%29+%2B+sqrt%28x-5%29+=+5\"\r\n" );
document.write( "\"sqrt%289%29+%2B+sqrt%289-5%29+=+5\"\r\n" );
document.write( "\"sqrt%289%29+%2B+sqrt%284%29+=+5\"\r\n" );
document.write( "\"3%2B2=5\"\r\n" );
document.write( "\"5=5\"\r\n" );
document.write( "\r\n" );
document.write( "So the solution is \"9\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "
\n" ); document.write( "
\n" );