The quadratic equation x^2 + 8x + 15 = 0 can be rewritten as the equation below, where p and q are constants. (x – p)^2 = q What

Question

The quadratic equation x^2 + 8x + 15 = 0 can be rewritten as the equation below, where p and q are constants.
(x – p)^2 = q
What is the value of p?

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Thành Công 5 years 2021-07-26T06:05:52+00:00 1 Answers 14 views 0

Answers ( )

  1. Verity
    0
    2021-07-26T06:07:36+00:00
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    Answer:

    p = -4 and q = 1

    Step-by-step explanation:

    Given

    x^2 + 8x + 15 = 0

    Required

    Rewrite as:

    (x - p)^2 =q

    x^2 + 8x + 15 = 0

    Subtract 15 from both sides

    x^2 + 8x + 15 - 15 = 0 - 15

    x^2 + 8x = - 15

    ———————————————————————–

    To make the equation a perfect square, follow these steps

    b = 8 —- the coefficient of x

    Divide both sides by 2:

    \frac{b}{2} = \frac{8}{2}

    \frac{b}{2} = 4

    Square both sides

    (\frac{b}{2})^2 = 4^2

    (\frac{b}{2})^2 = 16

    —————————————————————————————

    So, we add 16 t0 both sides of: x^2 + 8x = - 15

    x^2 + 8x + 16 = - 15 + 16

    x^2 + 8x + 16 = 1

    Factorize:

    x^2 + 4x + 4x+ 16 = 1

    x(x + 4) + 4(x + 4) = 1

    (x + 4) (x + 4) = 1

    (x + 4)^2 = 1

    By comparison to: (x - p)^2 =q

    -p = 4 and q = 1

    So, we have:

    p = -4 and q = 1

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )