Question

What two numbers add to 13 but multiply to negative 12?

Answer 1

9514 1404 393

Answer:

  13.8654599313 and -0.8654599313

Step-by-step explanation:

If one of the numbers is x, then the other is 13-x, and their product is ...

  x(13 -x) = -12

  x^2 -13x = 12 . . . . multiply by -1 and simplify

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

  (x -6.5)^2 = 54.25

  x -6.5 = √54.25

  x = 6.5 +√54.25 ≈ 13.8654599313

and the other number is ...

  13 -x = 13 -13.8654599313 = -0.8654599313

The two numbers are 13.8654599313 and -0.8654599313.