xy = -14
x + y = -3
\(xy = -14\)
\(\frac{xy}{x} = \frac{-14}{x}\)
\(y = \frac{-14}{x}\)
\(x + y = -3\)
\(x + \frac{-14}{x} = -3\)
\(\frac{x^{2}}{x} + \frac{-14}{x} = -3\)
\(\frac{x^{2} - 14}{x} = -3\)
\(x^{2} - 14 = -3x\)
\(x^{2} + 3x - 14 = 0\)
\(x = \frac{-(3) \± \sqrt{(3)^{2} - 4(1)(-14)}}{2(1)}\)
\(x = \frac{-3 \± \sqrt{9 + 56}}{2}\)
\(x = \frac{-3 \± \sqrt{65}}{2}\)
\(x = \frac{-3 \± 8.06}{2}\)
\(x = -1.5 \± 4.03\)
\(x = -1.5 + 4.03\) \(or\) \(x = -1.5 - 4.03\)
\(x = 2.53\) \(or\) \(x = -5.53\)
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.
