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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