Question 1177207
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            The  "solution"  by  @MathLover1 is irrelevant to the posed problem,  since she solved  DIFFERENT  problem.


            So I came to bring the  TRUE  solution.




The sum of two numbers is {{{-34}}}. 

{{{x+y=-34}}}
{{{y=-34-x}}}


their product: 

{{{xy}}}...........substitute {{{y}}}


={{{x(-34-x)}}}
={{{-34x-x^2}}}............complete square
={{{-(x^2+34x+b^2)-(-b^2)}}}........{{{b=-34/2=-17}}}
={{{-(x^2+34x+17^2)+17^2}}}
={{{-(x+17)^2+289}}}


=> the numbers are: &nbsp;&nbsp;x= -17 &nbsp;&nbsp;and  &nbsp;&nbsp;y= -17.   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U>


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Solved.