xy = -112
x + y = -54
\(xy = -112\)
\(\frac{xy}{x} = \frac{-112}{x}\)
\(y = \frac{-112}{x}\)
\(x + y = -54\)
\(x + \frac{-112}{x} = -54\)
\(\frac{x^{2}}{x} + \frac{-112}{x} = -54\)
\(\frac{x^{2} - 112}{x} = -54\)
\(x^{2} - 112 = -54x\)
\(x^{2} + 54x - 112 = 0\)
\(x^{2} + 56x - 2x - 112 = 0\)
\(x(x) + x(56) - 2(x) - 2(56) = 0\)
\(x(x + 56) - 2(x + 56) = 0\)
\((x - 2)(x + 56) = 0\)
\(x - 2 = 0\) \(or\) \(x + 56 = 0\)
\(x = 2\) \(or\) \(x = -56\)
x + y = -54
2 + y = -54
- 2 - 2
y = -56
(x, y) = (2, -56)
or
x + y = -54
-56 + y = -54
+ 56 + 56
y = 2
(x, y) = (-56, 2)
The two numbers that multiply to -12 and add up to -54 are -56 and 2.
