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28 February, 20:46

What two numbers add to 15 and multiply to negative 312?

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Answers (1)
  1. 28 February, 21:52
    0
    X + y = 15

    xy = - 312

    x + y = 15

    x - x + y = - x + 15

    y = - x + 15

    xy = - 312

    x (-x + 15) = - 312

    x (-x) + x (15) = - 312

    -x² + 15x = - 312

    -x² + 15x + 312 = 0

    -1 (x²) - 1 (-15x) - 1 (312) = 0

    -1 (x² - 15x + 312) = 0

    -1 - 1

    x² - 15x + 312 = 0

    x = - (-15) ± √ ((-15) ² - 4 (1) (312))

    2 (1)

    x = 15 ± √ (225 - 1248)

    2

    x = 15 ± √ (-1023)

    2

    x = 15 ± 31.984i

    2

    x = 7.5 ± 15.992

    x = 7.5 + 15.992 or x = 7.5 - 15.992

    x = 23.492 or x = - 8.492

    x + y = 15

    23.492 + y = 15

    - 23.492 - 23.492

    y = - 8.492

    (x, y) = (23.492, - 8.492)

    or

    x + y = 15

    -8.492 + y = 15

    + 8.492 + 8.492

    y = 23.492

    (x, y) = (-8.492, 23.492)

    The two numbers that add up to 15 and mutliply to - 312 are - 8.492 and 23.492.
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