Question 1168261
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<U>ANSWER</U>.  The numbers are -8 and 5.



Two solutions are possible.


One solution is to guess the answer.

A person familiar with the multiplication table, can do it mentally (inside his mind, without using equations) in 5 seconds.



Alternative solution is algebraic.


    x + y = -3     (1)

    xy = -40.      (2)


From equation (1), express  y = -3 - x  and substitute to equation (2)

    x*(-3-x) = -40.


Simplify it and reduce to the standard form of the quadratic equation

    -x^2 - 3x + 40 = 0,   or, equivalently,

     x^2 + 3x - 40 = 0.


You may solve the last equation EITHER factoring

    (x+8)*(x-5) = 0

OR using the quadratic formula

    {{{x[1,2]}}} = {{{(-3 +- sqrt(3^2 - 4*(-40)))/2}}} = {{{(-3 +- sqrt(169))/2}}} = {{{(-3 +- 13)/2}}}.


It gives you the answer that is placed at the very beginning of my post.
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Solved, explained and completed.