x + y = -7
xy = 10
[tex]xy = -7[/tex]
[tex]\frac{xy}{x} = \frac{-7}{x}[/tex]
[tex]y = \frac{-7}{x}[/tex]
[tex]x + y = -7[/tex]
[tex]x + \frac{-7}{x} = -7[/tex]
[tex]\frac{x^{2}}{x} + \frac{-7}{x} = 7[/tex]
[tex]\frac{x^{2} - 7}{x} = -7[/tex]
[tex]x^{2} - 7 = -7x[/tex]
[tex]x^{2} + 7x - 7 = 0[/tex]
[tex]x = \frac{-(7) \± \sqrt{(7)^{2} - 4(1)(-7)}}{2(1)}[/tex]
[tex]x = \frac{-7 \± \sqrt{49 + 28}}{2}[/tex]
[tex]x = \frac{-7 \± \sqrt{77}}{2}[/tex]
[tex]x = \frac{-7 \± 8.8}{2}[/tex]
[tex]x = \frac{-7 + 8.8}{2}[/tex] [tex]or[/tex] [tex]x = \frac{-7 - 8.8}{2}[/tex]
[tex]x = \frac{1.8}{2}[/tex] [tex]or[/tex] [tex]x = \frac{-15.8}{2}[/tex]
[tex]x = 0.9[/tex] [tex]or[/tex] [tex]x = -7.9[/tex]
x + y = -7
0.9 + y = -7
- 0.9 - 0.9
y = -7.9
(x, y) = (0.9, -7.9)
or
x + y = -7
-7.9 + y = -7
+ 7.9 + 7.9
y = 0.9
(x, y) = (-7.9, 0.9)
The two numbers that add up to -7 and multiply to -10 are -7.9 and 0.9.
