xy = -112
x + y = -54
[tex]xy = -112[/tex]
[tex]\frac{xy}{x} = \frac{-112}{x}[/tex]
[tex]y = \frac{-112}{x}[/tex]
[tex]x + y = -54[/tex]
[tex]x + \frac{-112}{x} = -54[/tex]
[tex]\frac{x^{2}}{x} + \frac{-112}{x} = -54[/tex]
[tex]\frac{x^{2} - 112}{x} = -54[/tex]
[tex]x^{2} - 112 = -54x[/tex]
[tex]x^{2} + 54x - 112 = 0[/tex]
[tex]x^{2} + 56x - 2x - 112 = 0[/tex]
[tex]x(x) + x(56) - 2(x) - 2(56) = 0[/tex]
[tex]x(x + 56) - 2(x + 56) = 0[/tex]
[tex](x - 2)(x + 56) = 0[/tex]
[tex]x - 2 = 0[/tex] [tex]or[/tex] [tex]x + 56 = 0[/tex]
[tex]x = 2[/tex] [tex]or[/tex] [tex]x = -56[/tex]
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.
