document.write( "Question 208735: Hi, could you please help me out?\r
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Algebra.Com's Answer #157859 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( "There are two radical terms. Choose\r\n" );
document.write( "one of them to isolate, usually it's \r\n" );
document.write( "easier to choose the more complicated.\r\n" );
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document.write( "Isolate one term with a radical:\r\n" );
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document.write( "\"sqrt%282x%2B3%29+=+1+%2B+sqrt%28x%2B1%29\"\r\n" );
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document.write( "Put parentheses around both sides and\r\n" );
document.write( "square them:\r\n" );
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document.write( "\"%28sqrt%282x%2B3%29%29%5E2+=+%281+%2B+sqrt%28x%2B1%29%29%5E2\"\r\n" );
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document.write( "It's easy to square the left side because it\r\n" );
document.write( "just has one term, a square root term, so you\r\n" );
document.write( "just take away the radical. \r\n" );
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document.write( "However the right side is not so easy to\r\n" );
document.write( "square because it contains TWO terms.  You \r\n" );
document.write( "have to put it down twice and FOIL it out:\r\n" );
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document.write( "\"2x%2B3+=+%281+%2B+sqrt%28x%2B1%29%29%281%2Bsqrt%28x%2B1%29%29\"\r\n" );
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document.write( "\"2x%2B3+=+1%2Bsqrt%28x%2B1%29%2Bsqrt%28x%2B1%29%2B+%28sqrt%28x%2B1%29%5E2%29\"\r\n" );
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document.write( "\"2x%2B3+=+1%2B2sqrt%28x%2B1%29%2B+%28x%2B1%29\"\r\n" );
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document.write( "\"2x%2B3+=+1%2B2sqrt%28x%2B1%29%2Bx%2B1\"\r\n" );
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document.write( "\"2x%2B3+=+2%2B2sqrt%28x%2B1%29%2Bx\"\r\n" );
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document.write( "Now you have one radical term instead of two\r\n" );
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document.write( "Isolate the one term with a radical. I'll\r\n" );
document.write( "isolate it on the right since that's the\r\n" );
document.write( "side it's already on. So as before, put parentheses \r\n" );
document.write( "around both sides and square them:\r\n" );
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document.write( "\"x%2B1+=+2sqrt%28x%2B1%29\"\r\n" );
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document.write( "Square both sides again:\r\n" );
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document.write( "\"%28x%2B1%29%5E2+=+%282sqrt%28x%2B1%29%29%5E2\"\r\n" );
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document.write( "\"%28x%2B1%29%28x%2B1%29+=+4%28x%2B1%29\"\r\n" );
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document.write( "\"x%5E2%2Bx%2Bx%2B1+=+4x%2B4\"\r\n" );
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document.write( "\"x%5E2%2B2x%2B1=4x%2B4\"\r\n" );
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document.write( "THAT'S A QUADRATIC SO GET 0 on the right:\r\n" );
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document.write( "\"++x%5E2-2x-3=0++\"\r\n" );
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document.write( "Factor the left side:\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 because sometimes \r\n" );
document.write( "we get extraneous or bogus solutions.\r\n" );
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document.write( "Checking \"x=3\" in the original equation:\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%2A3%2B3%29+-+sqrt%283%2B1%29+=1\"\r\n" );
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document.write( "\"sqrt%286%2B3%29+-+sqrt%284%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( "That checks, too, so \"x=3\" is a valid solution.\r\n" );
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document.write( "Checking \"x=-1\" in the original equation:\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%2A%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+-+sqrt%280%29+=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( "That checks so x=-1 is also a valid solution.\r\n" );
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document.write( "There are two solutions, 3 and -1.\r\n" );
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document.write( "Edwin
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