Question

What two numbers multiply to get -48 and add to get 2

Answer 1

xy = -48
x + y = 2

$xy = -48$
$\frac{xy}{x} = \frac{-48}{x}$
$y = \frac{-48}{x}$

$x + y = 2$
$x + \frac{-48}{x} = 2$
$\frac{x^{2}}{x} + \frac{-48}{x} = 2$
$\frac{x^{2} - 48}{x} = 2$
$2x = x^{2} - 48$
$0 = x^{2} - 2x - 48$
$x = \frac{-(-2) \± \sqrt{(-2)^{2} - 4(1)(-48)}}{2(1)}$
$x = \frac{2 \± \sqrt{4 + 192}}{2}$
$x = \frac{2 \± \sqrt{196}}{2}$
$x = \frac{2 \± 14}{2}$
$x = \frac{1 \± 7}{1}$
$x =\frac{1 + 7}{1}$    $or$    $x = \frac{1 - 7}{1}$
$x = \frac{8}{1}$    $or$    $x = \frac{-6}{1}$
$x = 8$    $or$    $x = -6$

  x + y = 2
  8 + y = 2
- 8        - 8
        y = -6
(x, y) = (8, -6)

    x + y = 2
   -6 + y = 2
 + 6       + 6
          y = 8
    (x, y) = (-6, 8)

The two numbers that multiply to -48 and add up to 2 are the numbers -6 and 8.