xy = -126
x + y = -65
\(xy = -126\)
\(\frac{xy}{x} = \frac{-126}{x}\)
\(y = \frac{-126}{x}\)
\(x + y = -65\)
\(x + \frac{-126}{x} = -65\)
\(\frac{x^{2}}{x} + \frac{-126}{x} = -65\)
\(\frac{x^{2} - 126}{x} = -65\)
\(-65x = x^{2} - 126\)
\(0 = x^{2} + 65x - 126\)
\(x = \frac{-(65) \+ \sqrt{(65)^{2} - 4(1)(-126)}}{2(1)}\)
\(x = \frac{-65 \± \sqrt{4225 + 504}}{2}\)
\(x = \frac{-65 \± \sqrt{4729}}{2}\)
\(x = \frac{-65 \± 68.8}{2}\)
\(x = \frac{-65 + 68.8}{2}\) \(or\) \(x = \frac{-65 - 68.8}{2}\)
\(x = \frac{3.8}{2}\) \(or\) \(x = \frac{-133.8}{2}\)
\(x = 1.9\) \(or\) \(x = -66.9\)
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.
