x + y = -54
xy = -16
\(xy = -16\)
\(\frac{xy}{x} = \frac[-16}{x}\)
\(y = \frac{-16}{x}\)
\(x + y = -54\)
\(x + \frac{-16}{x} = -54\)
\(\frac{x^{2}}{x} + \frac{-16}{x} = -54\)
\(\frac{x^{2} - 16}{x} = -54\)
\(x^{2} - 16 = -54x\)
\(x^{2} + 54x - 16 = 0\)
\(x = \frac{-(54) \± \sqrt{(54)^{2} - 4(1)(-16)}}{2(1)}\)
\(x = \frac{-54 \± \sqrt{2916 + 64}}{2}\)
\(x = \frac{-54 \± \sqrt{2980}}{2}\)
\(x = \frac{-54 \± 59.6}{2}\)
\(x = -27 \± 29.8\)
\(x = -27 + 29.8\) \(or\) \(x = -27 - 29.8\)
\(x = 2.8\) \(or\) \(x = 56.8\)
x + y = -54
2.8 + y = -54
- 2.8 - 2.8
y = -56.8
(x, y) = (2.8, -56.8)
or
x + y = -54
-56.8 + y = -54
+ 56.8 + 56.8
y = 2.8
(x, y) = (-56.8, 2.8)
The two numbers that add up to -54 and multiply to -16 are -56.8 and 2.8.
