document.write( "Question 1134697: Find two numbers whose sum is -5 and whose product is -24. \n" ); document.write( "

Algebra.Com's Answer #752156 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "The standard way is to write a quadratic equation\r\n" );
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document.write( "    x*(-5 - x) = -24,\r\n" );
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document.write( "where x is one of the two numbers and -5 - x is the other number.\r\n" );
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document.write( "Then you transform the equation into the simpler equivalent form\r\n" );
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document.write( "    x*(x + 5) = 24,\r\n" );
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document.write( "    x^2 + 5x - 24 = 0.\r\n" );
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document.write( "At this point, you can find the solution by using the quadratic formula or by factoring\r\n" );
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document.write( "    (x+8)*(x-3) = 0.\r\n" );
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document.write( "The numbers are -8 and 3.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is much simpler way to solve the problem MENTALLY without using equations.\r
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document.write( "In such problems, as a rule, the solutions are integer numbers.\r\n" );
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document.write( "So, you try guessing the factors of the number -24 that sum up to -5.\r\n" );
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document.write( "You will try  24 = 12*2 = 6*4 = 8*3  and very fast you will find the ANSWER:\r\n" );
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document.write( "    the numbers are  -8  and  3,  exactly the same as in the solution above.\r\n" );
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\n" ); document.write( "\n" ); document.write( "After solving one - two - three such problems, you will be able to guess the answer MENTALLY and MOMENTARILY.\r
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\n" ); document.write( "\n" ); document.write( "demonstrating a good style solving such problems.\r
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\n" ); document.write( "\n" ); document.write( "But in that cases when such an approach does not work, you must apply the full scale solution using quadratic equations.\r
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