document.write( "Question 916182: A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.
\n" ); document.write( "Please help me to solve this problem which is based on the quadratic equation. \n" ); document.write( "
Algebra.Com's Answer #555942 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.
\n" ); document.write( "Please help me to solve this problem which is based on the quadratic equation.
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document.write( "n = the number\r\n" );
document.write( "x = smaller part\r\n" );
document.write( "n-x = larger part\r\n" );
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\n" ); document.write( "the sum of the squares of the two parts is 20
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document.write( "\"x%5E2%2B%28n-x%29%5E2=20\"\r\n" );
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\n" ); document.write( "The square of the larger part is 8 times the smaller part
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document.write( "\"%28n-x%29%5E2=8x\"\r\n" );
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document.write( "So we have this system of equations to solve:\r\n" );
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document.write( "\"system%28x%5E2%2B%28n-x%29%5E2=20%2C%28n-x%29%5E2=8x%29\"\r\n" );
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document.write( "Using the second, substitute 8x for (n-x)2 in the first\r\n" );
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document.write( "\"x%5E2%2B8x=20\"\r\n" );
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document.write( "Get 0 on the right by subtracting 20 from both sides:\r\n" );
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document.write( "\"x%5E2%2B8x-20=0\"\r\n" );
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document.write( "Factor:\r\n" );
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document.write( "\"%28x-2%29%28x%2B10%29=0\"\r\n" );
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document.write( "Use the zero-factor property by setting each factor = 0\r\n" );
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document.write( "x-2 = 0;   x+10 = 0\r\n" );
document.write( "  x = 2       x = -10\r\n" );
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document.write( "We ignore the negative answer. \r\n" );
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document.write( "x = smaller part = 2\r\n" );
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\n" ); document.write( " find the number.
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document.write( "Substitute x = 2 in\r\n" );
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document.write( "\"%28n-x%29%5E2=8x\"\r\n" );
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document.write( "\"%28n-2%29%5E2=8%282%29\"\r\n" );
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document.write( "\"%28n-2%29%5E2=16\"\r\n" );
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document.write( "Use the principle of square roots:\r\n" );
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document.write( "\"n-2=+%22%22%2B-sqrt%2816%29\"\r\n" );
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document.write( "\"n-2+=+%22%22+%2B-+4\"\r\n" );
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document.write( "Add 2 to both sides\r\n" );
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document.write( "\"n=+%222%22+%2B-+4\"\r\n" );
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document.write( "Using the +, we get 2+4 = 6\r\n" );
document.write( "Using the -, we get 2-4 = -2\r\n" );
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document.write( "We ignore the negative answer.\r\n" );
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document.write( "Solution: 6\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "The two parts of 6 are 2 and 4\r\n" );
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\n" ); document.write( "the sum of the squares of the two parts is 20.
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document.write( "42+22 = 16 + 4 = 20\r\n" );
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document.write( "That checks.\r\n" );
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\n" ); document.write( "The square of the larger part is 8 times the smaller part
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document.write( "42 = 16 and 16 = (8)(2)\r\n" );
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document.write( "So that checks.\r\n" );
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document.write( "Edwin
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