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

x + y = -24
xy = -24

[tex]xy = -24[/tex]
[tex]\frac{xy}{x} = \frac{-24}{x}[/tex]
[tex]y = \frac{-24}{x}[/tex]

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

  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

[tex]xy = -24[/tex]
[tex]\frac{xy}{x} = \frac{-24}{x}[/tex]
[tex]y = \frac{-24}{x}[/tex]

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

  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.