document.write( "Question 661043: Hello! Can you please solve this question right away since I need this immediately for tomorrow:\r
\n" ); document.write( "\n" ); document.write( "Instruction(s): Find all real solutions in each equation.\r
\n" ); document.write( "\n" ); document.write( "√(x-3)+1=√(x+2)\r
\n" ); document.write( "\n" ); document.write( "Thanks for answering!!! \n" ); document.write( "
Algebra.Com's Answer #411455 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( " ___        ___\r\n" );
document.write( "√x-3 + 1 = √x+2\r\n" );
document.write( "\r\n" );
document.write( "You have one of the radical terms already \r\n" );
document.write( "isolated on the right, so we can go ahead and\r\n" );
document.write( "square both sides:\r\n" );
document.write( "\r\n" );
document.write( "  ___           ___\r\n" );
document.write( "(√x-3 + 1)² = (√x+2)²\r\n" );
document.write( "\r\n" );
document.write( "It's easy to square the right side by just removing \r\n" );
document.write( "the radical and the exponent and just get x+2.\r\n" );
document.write( "\r\n" );
document.write( "  ___          \r\n" );
document.write( "(√x-3 + 1)² = x+2\r\n" );
document.write( "\r\n" );
document.write( "But to square the left side is not so easy because \r\n" );
document.write( "it has two terms:\r\n" );
document.write( "  ___           ___       ___\r\n" );
document.write( "(√x-3 + 1)² = (√x-3 + 1)(√x-3 + 1) \r\n" );
document.write( "\r\n" );
document.write( "So we have to use FOIL: \r\n" );
document.write( " ___ ___    ___    ___\r\n" );
document.write( "√x-3√x-3 + √x-3 + √x-3 + 1\r\n" );
document.write( "  ___       ___\r\n" );
document.write( "(√x-3)² + 2√x-3 + 1\r\n" );
document.write( "            ___\r\n" );
document.write( "  x-3   + 2√x-3 + 1\r\n" );
document.write( "            ___\r\n" );
document.write( "  x - 2 + 2√x-3\r\n" );
document.write( "\r\n" );
document.write( "So now our equation:\r\n" );
document.write( "\r\n" );
document.write( "    ___          \r\n" );
document.write( "  (√x-3 + 1)² = x+2\r\n" );
document.write( "\r\n" );
document.write( "becomes\r\n" );
document.write( "\r\n" );
document.write( "          ___\r\n" );
document.write( "x - 2 + 2√x-3 = x+2\r\n" );
document.write( "\r\n" );
document.write( "We isolate the radical term on the left \r\n" );
document.write( "         ___\r\n" );
document.write( "       2√x-3 = 4\r\n" );
document.write( "\r\n" );
document.write( "We can divide both sides by 2\r\n" );
document.write( "         ___\r\n" );
document.write( "        √x-3 = 2\r\n" );
document.write( "\r\n" );
document.write( "We square both sides:\r\n" );
document.write( "\r\n" );
document.write( "        ___\r\n" );
document.write( "      (√x-3)² = (2)²\r\n" );
document.write( "\r\n" );
document.write( "          x-3 = 4\r\n" );
document.write( "\r\n" );
document.write( "            x = 7\r\n" );
document.write( "\r\n" );
document.write( "That may or not be the solution.  So we\r\n" );
document.write( "must always check, because these equations\r\n" );
document.write( "may have bogus solutions (called \"extraneous\"),\r\n" );
document.write( "So we must check in the ORIGINAL equation:\r\n" );
document.write( "\r\n" );
document.write( " ___        ___\r\n" );
document.write( "√x-3 + 1 = √x+2\r\n" );
document.write( " ___        ___\r\n" );
document.write( "√7-3 + 1 = √7+2\r\n" );
document.write( "   _        _\r\n" );
document.write( "  √4 + 1 = √9   \r\n" );
document.write( "\r\n" );
document.write( "   2 + 1 = 3\r\n" );
document.write( "\r\n" );
document.write( "       3 = 3\r\n" );
document.write( "\r\n" );
document.write( "It checks, so the solution is x=7.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );