document.write( "Question 157511: \"sqrt%282x%2B3%29-sqrt%28x%2B1%29=1\" can someone explain this problem to me? \n" ); document.write( "
Algebra.Com's Answer #116063 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\"sqrt%282x%2B3%29-sqrt%28x%2B1%29=1\"
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document.write( "Isolate one of the square root terms on one side\r\n" );
document.write( "of the equation.  I will isolate the first term, \"sqrt%282x%2B3%29\"\r\n" );
document.write( "by adding \"sqrt%28x%2B1%29\" to both sides:\r\n" );
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document.write( "\"sqrt%282x%2B3%29=1-sqrt%28x%2B1%29\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28sqrt%282x%2B3%29%29%5E2=%281-sqrt%28x%2B1%29%29%5E2\"\r\n" );
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document.write( "The left side amounts to squaring a square root,\r\n" );
document.write( "which just amounts to taking away the radical.\r\n" );
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document.write( "The right side is not so easy.  Write \"%281-sqrt%28x%2B1%29%29%5E2\" as \"%281-sqrt%28x%2B1%29%29%281-sqrt%28x%2B1%29%29\"\r\n" );
document.write( "and use FOIL:\r\n" );
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document.write( "\"2x%2B3=%281-sqrt%28x%2B1%29%29%281-sqrt%28x%2B1%29%29\"\r\n" );
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document.write( "\"2x%2B3=1-sqrt%28x%2B1%29-sqrt%28x%2B1%29%2Bx%2B1\"\r\n" );
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document.write( "Combine the two middle terms, which are like terms, \r\n" );
document.write( "on the right:\r\n" );
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document.write( "\"2x%2B3=1-2sqrt%28x%2B1%29%2Bx%2B1\"\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "\"2x%2B3=2-2sqrt%28x%2B1%29%2Bx\"\r\n" );
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document.write( "Isolate the radical term on the left:\r\n" );
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document.write( "\"2sqrt%28x%2B1%29=2%2Bx-2x-3\"\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "\"2sqrt%28x%2B1%29=-1-x\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%282sqrt%28x%2B1%29%29%5E2=%28-1-x%29%5E2\"\r\n" );
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document.write( "\"2%5E2%28sqrt%28x%2B1%29%29%5E2=%28-1-x%29%28-1-x%29\"\r\n" );
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document.write( "\"4%28x%2B1%29=1%2Bx%2Bx%2Bx%5E2\"\r\n" );
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document.write( "\"4x%2B4=1%2B2x%2Bx%5E2\"\r\n" );
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document.write( "Get 0 on the left:\r\n" );
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document.write( "\"0=1%2B2x%2Bx%5E2-4x-4\"\r\n" );
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document.write( "\"0=x%5E2-2x-3\"\r\n" );
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document.write( "Switch sides:\r\n" );
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document.write( "\"x%5E2-2x-3=0\"\r\n" );
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document.write( "\"%28x-3%29%28x%2B1%29=0\"\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "\"x-3=0\" gives \"x=3\"\r\n" );
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document.write( "\"x%2B1=0\" gives \"x=-1\"\r\n" );
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document.write( "But we must check these because\r\n" );
document.write( "many times we get extraneous solutions:\r\n" );
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document.write( "Checking \"x=3\" in original:\r\n" );
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document.write( "\"sqrt%282x%2B3%29-sqrt%28x%2B1%29=1\"\r\n" );
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document.write( "\"sqrt%282%283%29%2B3%29-sqrt%283%2B1%29=1\"\r\n" );
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document.write( "\"sqrt%286%2B3%29-sqrt%283%2B1%29=1\"\r\n" );
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document.write( "\"sqrt%289%29-sqrt%284%29=1\"\r\n" );
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document.write( "\"3-2=1\"\r\n" );
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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( "But we must check these because\r\n" );
document.write( "many times we get extraneous solutions:\r\n" );
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document.write( "Checking \"x=-1\" in original:\r\n" );
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document.write( "\"sqrt%282x%2B3%29-sqrt%28x%2B1%29=1\"\r\n" );
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document.write( "\"sqrt%282%28-1%29%2B3%29-sqrt%28-1%2B1%29=1\"\r\n" );
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document.write( "\"sqrt%28-2%2B3%29-sqrt%280%29=1\"\r\n" );
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document.write( "\"sqrt%281%29-0=1\"\r\n" );
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document.write( "\"1-0=1\"\r\n" );
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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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