document.write( "Question 1194585: A positive number is one-half another number. The sum of the numbers is 28 less than the square of the smaller number. What are the numbers? \n" ); document.write( "

Algebra.Com's Answer #826815 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "A positive number is one-half another number. The sum of the numbers is 28 less
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document.write( "From the condition, it is clear that BOTH the NUMBERS are positive.\r\n" );
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document.write( "So, let x be the smaller of the two numbers; then the other number is 2x.\r\n" );
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document.write( "Next, write an equation as you read the problem\r\n" );
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document.write( "    x + 2x = x^2 - 28.\r\n" );
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document.write( "It is the same as\r\n" );
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document.write( "     3x   = x^2 - 28,\r\n" );
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document.write( "or\r\n" );
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document.write( "     x^2 - 3x - 28 = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (x-7)*(x+4) = 0.\r\n" );
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document.write( "The roots are 7 and -4, and because you are looking for positive solutions, \r\n" );
document.write( "you accept x= 7 and deny x= -4.\r\n" );
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document.write( "ANSWER.  The numbers are 7 and 14.\r\n" );
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