document.write( "Question 1168261: find two integers with a product of -40 and a sum of -3 \n" ); document.write( "

Algebra.Com's Answer #792869 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The numbers are -8 and 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Two solutions are possible.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "One solution is to guess the answer.\r\n" );
document.write( "\r\n" );
document.write( "A person familiar with the multiplication table, can do it mentally (inside his mind, without using equations) in 5 seconds.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Alternative solution is algebraic.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x + y = -3     (1)\r\n" );
document.write( "\r\n" );
document.write( "    xy = -40.      (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From equation (1), express  y = -3 - x  and substitute to equation (2)\r\n" );
document.write( "\r\n" );
document.write( "    x*(-3-x) = -40.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify it and reduce to the standard form of the quadratic equation\r\n" );
document.write( "\r\n" );
document.write( "    -x^2 - 3x + 40 = 0,   or, equivalently,\r\n" );
document.write( "\r\n" );
document.write( "     x^2 + 3x - 40 = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You may solve the last equation EITHER factoring\r\n" );
document.write( "\r\n" );
document.write( "    (x+8)*(x-5) = 0\r\n" );
document.write( "\r\n" );
document.write( "OR using the quadratic formula\r\n" );
document.write( "\r\n" );
document.write( "     =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives you the answer that is placed at the very beginning of my post.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved, explained and completed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );