Question

Which two numbers add up to -24 and multiple to -24

Answer 1

x + y = -24
xy = -24

$xy = -24$
$\frac{xy}{x} = \frac{-24}{x}$
$y = \frac{-24}{x}$

$x + y = -24$
$x + \frac{-24}{x} = -24$
$\frac{x^{2}}{x} + \frac{-24}{x} = -24$
$\frac{x^{2} - 24}{x} = -24$
$-24x = x^{2} - 24$
$0 = x^{2} + 24x - 24$
$x = \frac{-(24) \± \sqrt{(24)^{2} - 4(1)(-24)}}{2(1)}$
$x = \frac{-24 \± \sqrt{576 + 96}}{2}$
$x = \frac{-24 \± \sqrt{672}}{2}$
$x = \frac{-24 \± 4\sqrt{42}}{2}$
$x = -12 \± 2\sqrt{42}$
$x = -12 \± 2(6.5)$
$x = -12 \± 13$
$x = -12 + 13$    $or$    $x = -12 - 13$
$x = 1$    $or$    $x = -25$

  x + y = -24      or      x + y = -24
  1 + y = -24    or    -25 + y = -24
- 1           - 1         + 25        + 25
        y = -25        or         y = 1
  (x, y) = (1, -25)  or  (x, y) = (-25, 1)

The two numbers that add up to 24 are the numbers 1 and -25.

x + y = -24
xy = -24

$xy = -24$
$\frac{xy}{x} = \frac{-24}{x}$
$y = \frac{-24}{x}$

$x + y = -24$
$x + \frac{-24}{x} = -24$
$\frac{x^{2}}{x} + \frac{-24}{x} = -24$
$\frac{x^{2} - 24}{x} = -24$
$-24x = x^{2} - 24$
$0 = x^{2} + 24x - 24$
$x = \frac{-(24) \± \sqrt{(24)^{2} - 4(1)(-24)}}{2(1)}$
$x = \frac{-24 \± \sqrt{576 + 96}}{2}$
$x = \frac{-24 \± \sqrt{672}}{2}$
$x = \frac{-24 \± 4\sqrt{42}}{2}$
$x = -12 \± 2\sqrt{42}$
$x = -12 \± 2(6)$
$x = -12 \± 12$
$x = -12 + 12$    $or$    $x = -12 - 12$
$x = 0$    $or$    $x = -24$

  x + y = -24      or      x + y = -24
  0 + y = -24    or    -24 + y = -24
- 0           - 0         + 24        + 24
        y = 24         or         y = 0

The two numbers that multiply to -24 are the numbers 24 and 0.