document.write( "Question 204320: Three times the square of a certain postive number exceeds six times the number by nine. Find the number? \n" ); document.write( "
Algebra.Com's Answer #154255 by Edwin McCravy(20056)\"\" \"About 
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Edwin's solution and explanation:
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document.write( "Three times the square of a certain postive number exceeds\r\n" );
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document.write( "Let N be \"a certain positive number\" as well as \"the number\"  \r\n" );
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document.write( "Three times the square of N exceeds six times N by nine.\r\n" );
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document.write( "Let \"the square of N\" be N2.\r\n" );
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document.write( "Three times N2 exceeds six times N by nine.\r\n" );
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document.write( "Replace \"Three times N2 by 3N2.\r\n" );
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document.write( "3N2 exceeds six times N by nine.\r\n" );
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document.write( "Replace \"six times N\" by 6N\r\n" );
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document.write( "3N2 exceeds 6N by nine.\r\n" );
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document.write( "That means if you subtract them (larger minus smaller)\r\n" );
document.write( "you'll get 9.\r\n" );
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document.write( "The larger is the one that does the exceeding, 3N2,\r\n" );
document.write( "so the smaller one is 6N, so when we subtract them by putting\r\n" );
document.write( "a minus sign between them, we must get 9.\r\n" );
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document.write( "       3N2 - 6N = 9\r\n" );
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document.write( "   3N2 - 6N - 9 = 0\r\n" );
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document.write( " 3(N2 - 2N - 3) = 0\r\n" );
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document.write( "3(N - 3)(N + 1) = 0\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( " (N - 3)(N + 1) = 0\r\n" );
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document.write( "N - 3 = 0;    N + 1 = 0\r\n" );
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document.write( "    N = 3;        N = -1\r\n" );
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document.write( "Since the requirement \"a certain POSITIVE numbers\"\r\n" );
document.write( "was given we discared the -1 and the only solution\r\n" );
document.write( "is N = 3\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "Three times the square of 3 exceeds six times 3 by nine.\r\n" );
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document.write( "Three times 9 exceeds six times 3 by nine.\r\n" );
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document.write( "27 exceeds 6 times 3 by 9\r\n" );
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document.write( "27 exceeds 18 by 9\r\n" );
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document.write( "That is true.\r\n" );
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document.write( "Edwin
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