What two numbers multiply to get -48 and add to get 2

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.

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