Question

What two numbers multiply to negative 12 and add up to negative 13

Answer 1

−13.8654599313 and 0.8654599313

Explanation:

The two numbers of interest will be the solutions to ...

xy = -12

x +y = -13

Substituting for y, this becomes the quadratic ...

x(-13 -x) = -12

x^2 +13x = 12 . . . . . multiply by -1

x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square

(x +6.5)^2 = 54.25

x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5

x ≈ -13.865499313 or 0.8654599313

The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.