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igomit [66]
3 years ago
11

What adds up to -54 and multiplies to -16

Mathematics
1 answer:
Kaylis [27]3 years ago
8 0
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.
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