document.write( "Question 1060137: what two numbers whose product is minus−72 and whose sum is 21. These numbers will be the constants in the binomial factors. \n" ); document.write( "

Algebra.Com's Answer #675114 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let x = first number
\n" ); document.write( " y = 2nd number\r
\n" ); document.write( "\n" ); document.write( " $\"xy+=+-72\"$ (1)
\n" ); document.write( " $\"x%2By+=+21\"$ (2)\r
\n" ); document.write( "\n" ); document.write( "(1) —> $\"+y+=+-72%2Fx+\"$ (1a)\r
\n" ); document.write( "\n" ); document.write( "Substitute this into (2):
\n" ); document.write( " $\"+x+%2B+%28-72%2Fx%29+=+21+\"$
\n" ); document.write( " $\"+x%5E2+-72+=+21x+\"$ (multiplied both sides by 'x')
\n" ); document.write( " $\"+x%5E2+-+21x+-+72+=+0+\"$
\n" ); document.write( " $\"+%28x%2B3%29%28x-24%29+=+0+\"$ \r
\n" ); document.write( "\n" ); document.write( "So $\"+x=-3\"$ or $\"+x=24+\"$ \r
\n" ); document.write( "\n" ); document.write( "Using (1a):
\n" ); document.write( " $\"+x=-3\"$ —> $\"+y=24+\"$
\n" ); document.write( " $\"+x=24\"$ —> $\"+y=-3\"$ (the two answers just swap x & y, makes sense)
\n" ); document.write( "—
\n" ); document.write( "Ans: The two numbers are -3 and 24
\n" ); document.write( "—\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( " -3*24 = -72 (ok)
\n" ); document.write( " -3+24 = 21 (ok)
\n" ); document.write( "—\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );