Let the two numbers be represented by x and y. Then xy = 4 and x + y = -5.
Solving the first equation for y, we get y = 4/x.
Subbing 4/x for y in the second equation, we get x + 4/x = -5.
Multiplying all three terms by x removes the fractional term:
x^2 + 4 = -5x
Rearranging terms in descending powers of x: x^2 + 5x + 4 = 0
Factoring, (x+1)(x+4)=0, so that x = -1 and x= -4 are roots / solutions.
Note that (-1)(-4) = 4 and that (-1) + (-4) = -5, as required.
Two such numbers are {-1, -4).
