document.write( "Question 817886: Need to solve this equation by hand. Please help me. Thanks!\r
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Algebra.Com's Answer #492294 by Edwin McCravy(20055)\"\" \"About 
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document.write( "√2x+3 - √x+1 = 1\r\n" );
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document.write( "Isolate one of the radicals:\r\n" );
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document.write( "       √2x+3 = 1-√x+1\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "    (√2x+3)² = (1-√x+1)²\r\n" );
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document.write( "Squaring the left side takes away the radical\r\n" );
document.write( "Squaring the right side means to write the \r\n" );
document.write( "(expression twice\r\n" );
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document.write( "        2x+3 = (1-√x+1)(1-√x+1)\r\n" );
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document.write( "FOIL out the right side:\r\n" );
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document.write( "        2x+3 = 1-√x+1-√x+1+(√x+1)²\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "        2x+3 = 1-2√x+1+x+1\r\n" );
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document.write( "        2x+3 = 2+x-2√x+1\r\n" );
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document.write( "Isolate the radical term\r\n" );
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document.write( "         x+1 = -2√x+1\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "      (x+1)² = (-2√x+1)²\r\n" );
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document.write( "  (x+1)(x+1) = (-2)²(√x+1)²\r\n" );
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document.write( "    x²+x+x+1 = 4(x+1)\r\n" );
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document.write( "     x²+2x+1 = 4x+4\r\n" );
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document.write( "Get 0 on the right:\r\n" );
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document.write( "     x²-2x-3 = 0 \r\n" );
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document.write( "Factor the left side:\r\n" );
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document.write( "  (x-3)(x+1) = 0\r\n" );
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document.write( "Us zero-factor property:\r\n" );
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document.write( "  x-3 = 0;  x+1 = 0\r\n" );
document.write( "    x = 3;    x = -1\r\n" );
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document.write( "We must check for extraneous solutions:\r\n" );
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document.write( "Checking x = 3      \r\n" );
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document.write( "    √2x+3 - √x+1 = 1\r\n" );
document.write( "√2(3)+3 - √(3)+1 = 1\r\n" );
document.write( "     √6+3 - √3+1 = 1\r\n" );
document.write( "         √9 - √4 = 1\r\n" );
document.write( "           3 - 2 = 1\r\n" );
document.write( "               1 = 1\r\n" );
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document.write( "therefore x = 3 is a solution:\r\n" );
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document.write( "Checking x = -1      \r\n" );
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document.write( "      √2x+3 - √x+1 = 1\r\n" );
document.write( " √2(-1)+3 - √(1)+1 = 1\r\n" );
document.write( "     √-2+3 - √-1+1 = 1\r\n" );
document.write( "           √1 - √0 = 1\r\n" );
document.write( "             1 - 0 = 1\r\n" );
document.write( "                 1 = 1\r\n" );
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document.write( "Therefore x = -1 is also a solution.\r\n" );
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document.write( "Edwin
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