Respuesta :
xy = -14
x + y = -3
[tex]xy = -14[/tex]
[tex]\frac{xy}{x} = \frac{-14}{x}[/tex]
[tex]y = \frac{-14}{x}[/tex]
[tex]x + y = -3[/tex]
[tex]x + \frac{-14}{x} = -3[/tex]
[tex]\frac{x^{2}}{x} + \frac{-14}{x} = -3[/tex]
[tex]\frac{x^{2} - 14}{x} = -3[/tex]
[tex]x^{2} - 14 = -3x[/tex]
[tex]x^{2} + 3x - 14 = 0[/tex]
[tex]x = \frac{-(3) \± \sqrt{(3)^{2} - 4(1)(-14)}}{2(1)}[/tex]
[tex]x = \frac{-3 \± \sqrt{9 + 56}}{2}[/tex]
[tex]x = \frac{-3 \± \sqrt{65}}{2}[/tex]
[tex]x = \frac{-3 \± 8.06}{2}[/tex]
[tex]x = -1.5 \± 4.03[/tex]
[tex]x = -1.5 + 4.03[/tex] [tex]or[/tex] [tex]x = -1.5 - 4.03[/tex]
[tex]x = 2.53[/tex] [tex]or[/tex] [tex]x = -5.53[/tex]
x + y = -3
2.53 + y = -3
- 2.53 - 2.53
y = -5.53
(x, y) = (2.53, -5.53)
x + y = -3
-5.53 + y = -3
+ 5.53 + 5.53
y = 2.53
(x, y) = (-5.53, 2.53)
The two numbers that multiply to -14 and add up to -3 are -5.53 and 2.53.
x + y = -3
[tex]xy = -14[/tex]
[tex]\frac{xy}{x} = \frac{-14}{x}[/tex]
[tex]y = \frac{-14}{x}[/tex]
[tex]x + y = -3[/tex]
[tex]x + \frac{-14}{x} = -3[/tex]
[tex]\frac{x^{2}}{x} + \frac{-14}{x} = -3[/tex]
[tex]\frac{x^{2} - 14}{x} = -3[/tex]
[tex]x^{2} - 14 = -3x[/tex]
[tex]x^{2} + 3x - 14 = 0[/tex]
[tex]x = \frac{-(3) \± \sqrt{(3)^{2} - 4(1)(-14)}}{2(1)}[/tex]
[tex]x = \frac{-3 \± \sqrt{9 + 56}}{2}[/tex]
[tex]x = \frac{-3 \± \sqrt{65}}{2}[/tex]
[tex]x = \frac{-3 \± 8.06}{2}[/tex]
[tex]x = -1.5 \± 4.03[/tex]
[tex]x = -1.5 + 4.03[/tex] [tex]or[/tex] [tex]x = -1.5 - 4.03[/tex]
[tex]x = 2.53[/tex] [tex]or[/tex] [tex]x = -5.53[/tex]
x + y = -3
2.53 + y = -3
- 2.53 - 2.53
y = -5.53
(x, y) = (2.53, -5.53)
x + y = -3
-5.53 + y = -3
+ 5.53 + 5.53
y = 2.53
(x, y) = (-5.53, 2.53)
The two numbers that multiply to -14 and add up to -3 are -5.53 and 2.53.
