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.

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

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