document.write( "Question 464128: solve this equation by using the quadratic form
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Algebra.Com's Answer #317920 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor took your equation to be\r\n" );
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document.write( "\"3%2Fx-7%2B4%2Fx%2B2=1\"\r\n" );
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document.write( "because you didn't put parentheses around denominators to show\r\n" );
document.write( "where they start and where they end.  When you write algebra \r\n" );
document.write( "fractions all on one line, using a foward slash \"/\" for a fraction\r\n" );
document.write( "bar, you must put parentheses around both entire numerators and\r\n" );
document.write( "entire denominators any time there is more than just one letter \r\n" );
document.write( "or just one number in the numerator or denominator.  Otherwise\r\n" );
document.write( "there is no way to know where numerators and denominators start \r\n" );
document.write( "and end.  And when you don't put the parentheses in, it is \r\n" );
document.write( "understood that the numerator or denominator consists of just \r\n" );
document.write( "the one number or the one letter which is closest to the forward \r\n" );
document.write( "slash \"/\".  That's the way the other tutor interpreted your\r\n" );
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document.write( "I believe you intended for your equation to be this:\r\n" );
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document.write( "\"3%2F%28x-7%29%2B4%2F%28x%2B2%29=1\"\r\n" );
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document.write( "which you should have written all on one line as\r\n" );
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document.write( "3/(x-7)+4/(x+2)=1\r\n" );
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document.write( "That way we can tell that the -7 and +2 are parts of the \r\n" );
document.write( "denominators and not separate terms.  It was not necessary\r\n" );
document.write( "to place parentheses around the numerators because they\r\n" );
document.write( "just consist of one number each, 3 and 4, but it was necessary \r\n" );
document.write( "to put parentheses around the denominators.\r\n" );
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document.write( "Assuming you meant this:\r\n" );
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document.write( "\"3%2F%28x-7%29%2B4%2F%28x%2B2%29=1\",\r\n" );
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document.write( "write the 1 as \"1%2F1\" so everything will be a fraction:\r\n" );
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document.write( "\"3%2F%28x-7%29%2B4%2F%28x%2B2%29=1%2F1\"\r\n" );
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document.write( "The LCD is (x-7)(x+2) so we multiply through by \"red%28expr%28%28%28x-7%29%28x%2B2%29%29%2F1%29%29\"  \r\n" );
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document.write( "Then we cancel away the denominators:\r\n" );
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document.write( "We end up with no fractions at all\r\n" );
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document.write( "\"3%28x%2B2%29%2B4%28x-7%29=%28x-7%29%28x%2B2%29\"\r\n" );
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document.write( "Remove the parentheses:\r\n" );
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document.write( "\"3x%2B6%2B4x-28=x%5E2-5x-14\"\r\n" );
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document.write( "Collect like terms:\r\n" );
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document.write( "\"7x-22=x%5E2-5x-14\"\r\n" );
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document.write( "Get 0 on the left:\r\n" );
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document.write( "\"0=x%5E2-12x%2B8\"\r\n" );
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document.write( "Swap sides:\r\n" );
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document.write( "\"x%5E2-12x%2B8=0\"\r\n" );
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document.write( "Compare to \r\n" );
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document.write( "\"ax%B2%2Bbx%2Bc=0\"\r\n" );
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document.write( "And see that a=1, b=-12 and c=8.\r\n" );
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document.write( "Then use\r\n" );
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document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" \r\n" );
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document.write( "\"x+=+%2812+%2B-+sqrt%28144-32+%29%29%2F2+\"\r\n" );
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document.write( " \"x+=+%2812+%2B-+sqrt%28112+%29%29%2F2+\"\r\n" );
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document.write( "\"x+=+%2812+%2B-+sqrt%2816%2A7%29%29%2F2+\"\r\n" );
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document.write( "\"x+=+%2812+%2B-+4sqrt%287%29%29%2F2+\"\r\n" );
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document.write( "Factor 4 out of the top:\r\n" );
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document.write( "\"x+=+%284%283+%2B-+sqrt%287%29%29%29%2F2+\"\r\n" );
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document.write( "Divide top and bottom by 2\r\n" );
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document.write( "\"x+=+2%283+%2B-+sqrt%287%29%29+\"\r\n" );
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document.write( "or if you prefer:\r\n" );
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document.write( "\"x+=+6+%2B-+2sqrt%287%29%29+\"\r\n" );
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document.write( "The two exact solutions are\r\n" );
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document.write( "\"6+%2B+2sqrt%287%29%29+\" and \"6+-+2sqrt%287%29%29+\"\r\n" );
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document.write( "They are approximately 0.7 and 11.3.\r\n" );
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document.write( "Edwin
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