Question

What two numbers multiply to -112 and add up to -54

Answer 1

-56 and 2.

-56 x 2 = -112

-56 + 2 = -54

I found this out by first dividing -112 by two, and then figuring out what number that I should add to it to equal -54 :) Hope this helps!

Answer 2

Xy = -112
x + y = -54

$xy = -112$
$\frac{xy}{x} = \frac{-112}{x}$
$y = \frac{-112}{x}$

$x + y = -54$
$x + \frac{-112}{x} = -54$
$\frac{x^{2}}{x} + \frac{-112}{x} = -54$
$\frac{x^{2} - 112}{x} = -54$
$x^{2} - 112 = -54x$
$x^{2} + 54x - 112 = 0$
$x^{2} + 56x - 2x - 112 = 0$
$x(x) + x(56) - 2(x) - 2(56) = 0$
$x(x + 56) - 2(x + 56) = 0$
$(x - 2)(x + 56) = 0$
$x - 2 = 0$    $or$    $x + 56 = 0$
$x = 2$    $or$    $x = -56$

  x + y = -54
  2 + y = -54
- 2           - 2
        y = -56
  (x, y) = (2, -56)

          or

     x + y = -54
  -56 + y = -54
+ 56        + 56
           y = 2
    (x, y) = (-56, 2)

The two numbers that multiply to -12 and add up to -54 are -56 and 2.