xy = -36
x + y = 9
\(xy = -36\)
\(\frac{xy}{x} =\frac{-36}{x}\)
\(y = \frac{-36}{x}\)
\(x + y = 9\)
\(x + \frac{-36}{x} = 9\)
\(\frac{x^{2}}{x} + \frac{-36}{x} = 9\)
\(\frac{x^{2} - 36}{x} = 9\)
\(9x = x^{2} - 36\)
\(0 = x^{2} - 9x - 36\)
\(x = \frac{-(-9) \± \sqrt{(-9)^{2} - 4(1)(-36)}}{2(1)}\)
\(x = \frac{9 \± \sqrt{81 + 144}}{2}\)
\(x = \frac{9 \± \sqrt{225}}{2}\)
\(x = \frac{9 \± 15}{2}\)
\(x = \frac{9 + 15}{2}\) \(or\) \(x = \frac{9 - 15}{2}\)
\(x = \frac{24}{2}\) \(or\) \(x = \frac{-6}{2}\)
\(x = 12\) \(or\) \(x = -3\)
x + y = 9 or x + y = 9
12 + y = 9 or -3 + y = 9
- 12 - 12 + 3 + 3
y = -3 or y = 12
(x, y) = (12, -3) or (x, y) = (-3, 12)
The two numbers that add up to 9 and multiply to -36 are the numbers -3 and 12.
