xy = -48
x + y = 2
\(xy = -48\)
\(\frac{xy}{x} = \frac{-48}{x}\)
\(y = \frac{-48}{x}\)
\(x + y = 2\)
\(x + \frac{-48}{x} = 2\)
\(\frac{x^{2}}{x} + \frac{-48}{x} = 2\)
\(\frac{x^{2} - 48}{x} = 2\)
\(2x = x^{2} - 48\)
\(0 = x^{2} - 2x - 48\)
\(x = \frac{-(-2) \± \sqrt{(-2)^{2} - 4(1)(-48)}}{2(1)}\)
\(x = \frac{2 \± \sqrt{4 + 192}}{2}\)
\(x = \frac{2 \± \sqrt{196}}{2}\)
\(x = \frac{2 \± 14}{2}\)
\(x = \frac{1 \± 7}{1}\)
\(x =\frac{1 + 7}{1}\) \(or\) \(x = \frac{1 - 7}{1}\)
\(x = \frac{8}{1}\) \(or\) \(x = \frac{-6}{1}\)
\(x = 8\) \(or\) \(x = -6\)
x + y = 2
8 + y = 2
- 8 - 8
y = -6
(x, y) = (8, -6)
x + y = 2
-6 + y = 2
+ 6 + 6
y = 8
(x, y) = (-6, 8)
The two numbers that multiply to -48 and add up to 2 are the numbers -6 and 8.
