document.write( "Question 851006: What two numbers have a product that is twice their sum and have a difference of 2\r
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Algebra.Com's Answer #512594 by ramkikk66(644)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "What two numbers have a product that is twice their sum and have a difference of 2\r\n" );
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document.write( "Solution:\r\n" );
document.write( "Let one number be x. Then the other is x + 2.\r\n" );
document.write( "Sum of the numbers = \"x+%2B+x+%2B+2+=+2%2Ax+%2B+2\"\r\n" );
document.write( "Product = \"x%2A%28x+%2B+2%29+=+x%5E2+%2B+2%2Ax\"\r\n" );
document.write( "Since product is twice the sum,\r\n" );
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document.write( "\"x%5E2+%2B+2%2Ax+=+2%282%2Ax+%2B+2%29+=+4%2Ax+%2B+4\"\r\n" );
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document.write( "\"x%5E2+-+2%2Ax+-+4+=+0\"\r\n" );
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document.write( "Solution below:\r\n" );
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-2x%2B-4+=+0\") has the following solutons:\r\n" ); document.write( " \r\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"\r\n" ); document.write( " \r\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.\r\n" ); document.write( " \r\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-4=20\".\r\n" ); document.write( " \r\n" ); document.write( " Discriminant d=20 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--2%2B-sqrt%28+20+%29%29%2F2%5Ca\".\r\n" ); document.write( " \r\n" ); document.write( " \"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+3.23606797749979\"\r\n" ); document.write( " \"x%5B2%5D+=+%28-%28-2%29-sqrt%28+20+%29%29%2F2%5C1+=+-1.23606797749979\"\r\n" ); document.write( " \r\n" ); document.write( " Quadratic expression \"1x%5E2%2B-2x%2B-4\" can be factored:\r\n" ); document.write( " \"1x%5E2%2B-2x%2B-4+=+1%28x-3.23606797749979%29%2A%28x--1.23606797749979%29\"\r\n" ); document.write( " Again, the answer is: 3.23606797749979, -1.23606797749979.\n" ); document.write( "Here's your graph:\n" ); document.write( "\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-4+%29\"
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