document.write( "Question 662291: Please help me solve this equation for \"x\" : \"+b%5E2%2Ax%5E2%2B2%2Aa%2Ax+=+x%5E2+%2B+a%5E2+\" with \"b doesn't equal 1\". I'm really not sure where to start. Thanks so much! \n" ); document.write( "
Algebra.Com's Answer #412085 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "          b²x² + 2ax = x² + a²\r\n" );
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document.write( "b²x² - x² + 2ax - a² = 0\r\n" );
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document.write( " (b²-1)x² + 2ax - a² = 0\r\n" );
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document.write( "We have to use the quadratic formula, but since the\r\n" );
document.write( "quadratic formula contains the letters a and b, we\r\n" );
document.write( "change the letters in the formula to capital letters:\r\n" );
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document.write( "x = \"%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29+\"\r\n" );
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document.write( "Then A = b²-1, B = 2a, C = -a²\r\n" );
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document.write( "x = \r\n" );
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document.write( "[Now we can see why they said \"b does not equal 1\" because the\r\n" );
document.write( "denominator 2(b²-1) would be 0 if bcould equal 1, and we cannot\r\n" );
document.write( "divide by 0].\r\n" );
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document.write( "x = \"%28-2a+%2B-+sqrt%28+4a%5E2-4%28-a%5E2b%5E2%2Ba%5E2%29+%29%29%2F%282%28b%5E2-1%29%29+\"\r\n" );
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document.write( "x = \"%28-2a+%2B-+sqrt%28+4a%5E2%2B4a%5E2b%5E2-4a%5E2+%29%29%2F%282%28b%5E2-1%29%29+\"\r\n" );
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document.write( "x = \r\n" );
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document.write( "x = \"%28-2a+%2B-+sqrt%284a%5E2b%5E2+%29%29%2F%282%28b%5E2-1%29%29+\"\r\n" );
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document.write( "x = \"%28-2a+%2B-+2ab%29%2F%282%28b%5E2-1%29%29+\"\r\n" );
document.write( " \r\n" );
document.write( "x = \"%282a%28-1+%2B-+b%29%29%2F%282%28b%5E2-1%29%29+\"\r\n" );
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document.write( "x = \"%28cross%282%29a%28-1+%2B-+b%29%29%2F%28cross%282%29%28b%5E2-1%29%29+\"\r\n" );
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document.write( "x = \"%28a%28-1+%2B-+b%29%29%2F%28b%5E2-1%29+\"\r\n" );
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document.write( "There are two solutions, one using the + and one using the -\r\n" );
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document.write( "Solution 1:\r\n" );
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document.write( "x = \"%28a%28-1+%2B+b%29%29%2F%28b%5E2-1%29+\"\r\n" );
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document.write( "Reverse the terms in the parentheses in the numerator:\r\n" );
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document.write( "x = \"%28a%28b+-+1%29%29%2F%28b%5E2-1%29+\"\r\n" );
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document.write( "Factor the denominator:\r\n" );
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document.write( "x = \"%28a%28b+-+1%29%29%2F%28%28b-1%29%28b%2B1%29%29+\"\r\n" );
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document.write( "x = \"%28a%28cross%28b+-+1%29%29%29%2F%28%28cross%28b-1%29%29%28b%2B1%29%29+\"\r\n" );
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document.write( "x = \"a%2F%28b%2B1%29+\"\r\n" );
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document.write( "Solution 2:\r\n" );
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document.write( "x = \"%28a%28-1+-+b%29%29%2F%28b%5E2-1%29+\"\r\n" );
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document.write( "Reverse the terms in the parentheses in the numerator:\r\n" );
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document.write( "x = \"%28a%28-b+-+1%29%29%2F%28b%5E2-1%29+\"\r\n" );
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document.write( "Factor -1 out of the parentheses in the numerator:\r\n" );
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document.write( "x = \"%28a%28-1%29%28b+%2B+1%29%29%2F%28b%5E2-1%29+\"\r\n" );
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document.write( "x = \"%28-a%28b+%2B+1%29%29%2F%28b%5E2-1%29+\"\r\n" );
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document.write( "Factor the denominator:\r\n" );
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document.write( "x = \"%28-a%28b+%2B+1%29%29%2F%28%28b-1%29%28b%2B1%29%29+\"\r\n" );
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document.write( "x = \"%28-a%28cross%28b+%2B+1%29%29%29%2F%28%28b-1%29%28cross%28b%2B1%29%29%29+\"\r\n" );
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document.write( "x = \"-a%2F%28b-1%29+\"\r\n" );
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document.write( "So the solutions are \"a%2F%28b%2B1%29+\" and \"-a%2F%28b-1%29+\"\r\n" );
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document.write( "Edwin
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