document.write( "Question 1151192: put the equation 16x^2+y^2+64x-2y+67=0 into conic standard form \n" ); document.write( "
Algebra.Com's Answer #772839 by Edwin McCravy(20060)\"\" \"About 
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\"matrix%281%2C3%2C16x%5E2%2By%5E2%2B64x-2y%2B67%2C%22%22=%22%22%2C0%29\"\r\n" );
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document.write( "Swap the 2nd and 3rd terms on the left to get the terms together\r\n" );
document.write( "for each letter:\r\n" );
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document.write( "\"matrix%281%2C3%2C16x%5E2%2B64x%2By%5E2-2y%2B67%2C%22%22=%22%22%2C0%29\" \r\n" );
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document.write( "Subtract the constant term from both sides:\r\n" );
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document.write( "\"matrix%281%2C3%2C16x%5E2%2B64x%2By%5E2-2y%2C%22%22=%22%22%2C-67%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C16x%5E2%2B64x%2By%5E2-2y%2C%22%22=%22%22%2C-67%29\"\r\n" );
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document.write( "Factor out 16 out of the first two terms, and 1 out of\r\n" );
document.write( "the last two terms:\r\n" );
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document.write( "\"matrix%281%2C3%2C16%28x%5E2%2B4x%29%2B1%28y%5E2-2y%29%2C%22%22=%22%22%2C-67%29\"\r\n" );
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document.write( "We complete the square inside the first parentheses:\r\n" );
document.write( "1. Multiply the coefficient of x, which is 4, by one-half, getting 2.\r\n" );
document.write( "2. Square 2, getting 4.\r\n" );
document.write( "3. Add +4 at the end of the first parentheses.\r\n" );
document.write( "4. Since the number in front of the parentheses is 16, adding 4 inside\r\n" );
document.write( "   the parentheses amounts to adding 16∙4 or 64 to the left side, so\r\n" );
document.write( "   we add 64 to the right side:\r\n" );
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document.write( "\"matrix%281%2C3%2C16%28x%5E2%2B4x%2B4%29%2B1%28y%5E2-2y%29%2C%22%22=%22%22%2C-67%2B64%29\"\r\n" );
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document.write( "We complete the square inside the second parentheses:\r\n" );
document.write( "1. Multiply the coefficient of y, which is -2, by one-half, getting -1.\r\n" );
document.write( "2. Square -1, getting +1.\r\n" );
document.write( "3. Add +1 at the end of the first parentheses.\r\n" );
document.write( "4. Since the number in front of the parentheses is 1, adding 4 inside\r\n" );
document.write( "   the parentheses amounts to adding 1∙1 or 1 to the left side, so\r\n" );
document.write( "   we add 1 to the right side:\r\n" );
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document.write( "Next we factor the quadratics in the parentheses:\r\n" );
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document.write( "\"matrix%281%2C3%2C16%28x%2B2%29%28x%2B2%29%2B1%28y-1%29%28y-1%29%2C%22%22=%22%22%2C-2%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C16%28x%2B2%29%5E2%2B1%28y-1%29%5E2%2C%22%22=%22%22%2C-2%29\"\r\n" );
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document.write( "This does not represent a conic because the left side is positive\r\n" );
document.write( "and the right side is negative.  \r\n" );
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document.write( "We get 1 on the right side by dividing each term by -2\r\n" );
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document.write( "We divide top and bottom of the first fraction by 16\r\n" );
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document.write( "If this were a real conic, there would not be a negative number\r\n" );
document.write( "on the bottom of either term, but only positive numbers.\r\n" );
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document.write( "Did you copy the problem wrong?\r\n" );
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document.write( "Edwin
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