document.write( "Question 93556: Could you help me with this?\r
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Algebra.Com's Answer #68138 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Could you help me with this?\r\n" );
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document.write( "\"8sqrt%28x-1%29%2B1\" = \"x\"\r\n" );
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document.write( "Thank-you\r\n" );
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document.write( "\"8sqrt%28x-1%29%2B1\" = \"x\"\r\n" );
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document.write( "Add -1 to both sides to get the radical \r\n" );
document.write( "term alone on the left:\r\n" );
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document.write( "  \"8sqrt%28x-1%29\" = \"x-1\"\r\n" );
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document.write( "Square both sides of the equation:\r\n" );
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document.write( " \"+%28+8sqrt%28x-1%29+%29%5E2\" = \"+%28x-1%29%5E2+\"\r\n" );
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document.write( "\"8%5E2%28sqrt%28x-1%29%29%5E2\" = \"%28x-1%29%28x-1%29\"\r\n" );
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document.write( "\"64%28x-1%29\" = \"x%5E2-x-x%2B1\"\r\n" );
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document.write( "\"64x-64\" = \"x%5E2-2x%2B1\"\r\n" );
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document.write( "Switch left and right sides for convenience:\r\n" );
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document.write( "\"x%5E2-2x%2B1\" = \"64x-64\"\r\n" );
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document.write( "Get 0 on the right \r\n" );
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document.write( "\"x%5E2-66x%2B65\" = \"0\"\r\n" );
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document.write( "Factor left side by thinking of two whole numbers\r\n" );
document.write( "which have product 65 and sum 66, whch are 65 and 1:\r\n" );
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document.write( "\"%28x-65%29%28x-1%29\" = 0\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "\"x-65=0\" gives \"x=65\"\r\n" );
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document.write( "\"x-1=0\" gives \"x=1\"\r\n" );
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document.write( "However we must check these answers because radical\r\n" );
document.write( "equations often have extraneous answers, which are\r\n" );
document.write( "not solutions.  \r\n" );
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document.write( "Checking \"x=65\"\r\n" );
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document.write( "\"8sqrt%28x-1%29%2B1\" = \"x\"\r\n" );
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document.write( "\"8sqrt%2865-1%29%2B1\" = \"65\"\r\n" );
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document.write( "\"8sqrt%2864%29%2B1\" = \"65\"\r\n" );
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document.write( "\"8%288%29%2B1\" = \"65\"\r\n" );
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document.write( "\"64%2B1\" = \"65\"\r\n" );
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document.write( "\"65\" = \"65\"\r\n" );
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document.write( "So we know \"x=65\" is a valid solution.\r\n" );
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document.write( "Checking \"x=1\"\r\n" );
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document.write( "\"8sqrt%28x-1%29%2B1\" = \"x\"\r\n" );
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document.write( "\"8sqrt%281-1%29%2B1\" = \"1\"\r\n" );
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document.write( "\"8sqrt%280%29%2B1\" = \"1\"\r\n" );
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document.write( "\"8%280%29%2B1\" = \"1\"\r\n" );
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document.write( "\"0%2B1\" = \"1\"\r\n" );
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document.write( "\"1\" = \"1\"\r\n" );
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document.write( "So as it turns out, both \"x=1\" and \"x=65\"\r\n" );
document.write( "are valid solutions.\r\n" );
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document.write( "But be aware that this is not always the case.\r\n" );
document.write( "Sometimes when you get two answers, one of them\r\n" );
document.write( "will be a solution and the other will not check,\r\n" );
document.write( "and thus must be discarded; sometimes neither one \r\n" );
document.write( "is a solution and the equation has no solution.\r\n" );
document.write( "Just be sure to ALWAYS CHECK a RADICAL EQUATION.\r\n" );
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document.write( "Edwin
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