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Solve by completing the square;round to the nearest hundredth if necessary.

x^2-3x=4

Thanks so much.

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4 answers
  1. x^2 - 3 x = 4

    x^2 -3 x +(3/2)^2 = 4 + 9/4

    (x-1.5)^2 = (1/4)(16 + 9)

    (x-1.5)^2 = (1/4)(25) = 25/4

    x-3/2 = +/- 5/2

    x = 3/2 +/- 5/2

    x = 4 or x = -1

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  2. x ^ 2 - 3 x = 4

    The x-term coefficient = − 3

    The half of the x-term coefficient = − 3 / 2

    After squaring you have ( − 3 / 2 ) ^ 2= 9 / 4

    x ^ 2 - 3 x = 4

    Add 9 / 4 to both sides

    x ^ 2 - 3 x + 9 / 4 = 4 + 9 / 4

    x ^ 2 - 3 x + 9 / 4 = 16 / 4 + 9 / 4

    x ^ 2 - 3 x + 9 / 4 = 25 / 4

    Write the perfect square on the left side:

    ( x - 3 / 2 ) ^ 2 = 25 / 4

    Take the square root of both sides:

    x - 3 / 2 = sqroot ( 25 / 4 )

    x - 3 / 2 = ± 5 / 2 Add 3 / 2 to both sides

    x - 3 / 2 + 3 / 2 = ± 5 / 2 + 3 / 2

    x = ± 5 / 2 + 3 / 2

    x1 = 5 / 2 + 3 / 2 = 8 / 2 = 4

    x2 = - 5 / 2 + 3 / 2 = - 2 / 2 = - 1

    The solutions are :

    x = - 1 and x = 4

    ________
    Remark:

    x ^ 2 - 3 x + 9 / 4 = ( x - 3 / 2 ) ^ 2 becouse:

    ( x - 3 / 2 ) ^ 2 =

    x ^ 2 - 2 * x * 3 / 2 + ( 3 / 2 ) ^ 2 =

    x ^ 2 - x * 3 + 9 / 4 =

    x ^ 2 - 3 x + 9 / 4
    ______

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  3. 1.C
    2.C
    3.B
    4.D
    5.B

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  4. answers is correct!!! 100%

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