document.write( "Question 1208839: Find the real solutions of the radical equation. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "sqrt{(10+ 3•sqrt{x})} = sqrt{x}\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: (10 + 3•sqrt{x}) lies inside a bigger radicand.
\n" ); document.write( "

Algebra.Com's Answer #847321 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"sqrt%2810+%2B+3sqrt%28x%29%29+=+sqrt%28x%29\"\r\n" );
document.write( "\r\n" );
document.write( "Square both sides\r\n" );
document.write( "\r\n" );
document.write( "\"10+%2B+3sqrt%28x%29+=+x\"\r\n" );
document.write( "\r\n" );
document.write( "Isolate the square root term\r\n" );
document.write( "\r\n" );
document.write( "\"3sqrt%28x%29+=+x-10\"\r\n" );
document.write( "\r\n" );
document.write( "Square both sides\r\n" );
document.write( "\r\n" );
document.write( "\"9x+=+x%5E2-20x%2B100\"\r\n" );
document.write( "\r\n" );
document.write( "\"0+=+x%5E2-29x%2B100\"\r\n" );
document.write( "\r\n" );
document.write( "Factor the right side:\r\n" );
document.write( "\r\n" );
document.write( "\"0=%28x-25%29%28x-4%29\"\r\n" );
document.write( "\r\n" );
document.write( "x-25=0;   x-4=0\r\n" );
document.write( "   x=25;    x=4\r\n" );
document.write( "\r\n" );
document.write( "Check each potential solution in the original equation:\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%2810+%2B+3sqrt%2825%29%29+=+sqrt%2825%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%2810+%2B+3%2A5%29+=+5\"\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%2810%2B15%29=5\"\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%2825%29=5\"\r\n" );
document.write( "\r\n" );
document.write( "\"5=5\"\r\n" );
document.write( "\r\n" );
document.write( "So one solution is x = 25     <--ANSWER\r\n" );
document.write( "\r\n" );
document.write( "Checking x=4\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%2810+%2B+3sqrt%284%29%29+=+sqrt%284%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%2810+%2B+3%2A2%29+=+2\"\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%2810%2B6%29=2\"\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%2816%29=2\"\r\n" );
document.write( "\r\n" );
document.write( "\"4=2\"   <--FALSE!\r\n" );
document.write( "\r\n" );
document.write( "So 4 is NOT a solution.\r\n" );
document.write( "\r\n" );
document.write( "The only solution is x = 25\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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