xy = -126
x + y = -65
[tex]xy = -126[/tex]
[tex]\frac{xy}{x} = \frac{-126}{x}[/tex]
[tex]y = \frac{-126}{x}[/tex]
[tex]x + y = -65[/tex]
[tex]x + \frac{-126}{x} = -65[/tex]
[tex]\frac{x^{2}}{x} + \frac{-126}{x} = -65[/tex]
[tex]\frac{x^{2} - 126}{x} = -65[/tex]
[tex]-65x = x^{2} - 126[/tex]
[tex]0 = x^{2} + 65x - 126[/tex]
[tex]x = \frac{-(65) \+ \sqrt{(65)^{2} - 4(1)(-126)}}{2(1)}[/tex]
[tex]x = \frac{-65 \± \sqrt{4225 + 504}}{2}[/tex]
[tex]x = \frac{-65 \± \sqrt{4729}}{2}[/tex]
[tex]x = \frac{-65 \± 68.8}{2}[/tex]
[tex]x = \frac{-65 + 68.8}{2}[/tex] [tex]or[/tex] [tex]x = \frac{-65 - 68.8}{2}[/tex]
[tex]x = \frac{3.8}{2}[/tex] [tex]or[/tex] [tex]x = \frac{-133.8}{2}[/tex]
[tex]x = 1.9[/tex] [tex]or[/tex] [tex]x = -66.9[/tex]
x + y = -65
1.9 + y = -65
- 1.9 - 1.9
y = -66.9
(x, y) = (1.9, -66.9)
or
x + y = -65
-66.9 + y = -65
+ 66.9 + 66.9
y = 1.9
(x, y) = (-66.9, 1.9)
The two numbers that add up to -65 and can multiply to -126 are the numbers -66.9 and 1.9.
