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17 November, 08:05

Completing the square X^2+8x+3=0

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Answers (2)
  1. 17 November, 10:33
    0
    Solution by completing the square for:

    2+8+3=0

    x

    2

    +

    8

    x

    +

    3

    =

    0

    Keep

    x

    terms on the left and move

    the constant to the right side

    by subtracting it on both sides

    2+8=-3

    x

    2

    +

    8

    x

    =

    -

    3

    Take half of the

    x

    term and square it

    [8⋅12]2=16

    [

    8



    1

    2

    ]

    2

    =

    16

    then add the result to both sides

    2+8+16=-3+16

    x

    2

    +

    8

    x

    +

    16

    =

    -

    3

    +

    16

    Rewrite the perfect square on the left

    (+4) 2=-3+16

    (

    x

    +

    4

    )

    2

    =

    -

    3

    +

    16

    and combine terms on the right

    (+4) 2=13

    (

    x

    +

    4

    )

    2

    =

    13

    Take the square root of both sides

    +4=±13‾‾‾√

    x

    +

    4

    =

    ±

    13

    Simplify the Radical term (1):

    +4=±13‾‾‾√

    x

    +

    4

    =

    ±

    13

    Isolate the x on the left side and

    solve for x (1)

    =-4±13‾‾‾√

    x

    =

    -

    4

    ±

    13

    therefore (2)

    =-4+13‾‾‾√

    x

    =

    -

    4

    +

    13

    =-4-13‾‾‾√

    x

    =

    -

    4

    -

    13

    which becomes

    =-0.394449

    x

    =

    -

    0.394449

    =-7.60555
  2. 17 November, 11:54
    0
    (x + 4) ² - 13 = 0

    Step-by-step explanation:

    Completing the square means to create a quadratic with the numbers that have a variable.

    Here, that is x² + 8x: (x² + 8x + y²) = (x + y) ².

    Since 8x is the 2xy in this equation, that means 2y is 8, therefore, y is 4.

    So, completing the square gives us (x + 4) ² + 3 = 0.

    But, because we did this, we have an extra 16 in the equation, so we have to subtract that.

    That will look like: (x + 4) ² - 13 = 0.
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