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Math Help - completing square

  1. #1
    Junior Member
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    completing square

    help........

    i have Three questions which i really don't know how to do
    pls help me!!
    solve the given quadratic equations by completing the square.
    <br />
(1)----v(v + 2) = 15<br />
    ---------------------------------------------------------------------
    <br />
(2)----5T^2 - 10T + 4 = 0<br />

    (3)In machine design. in finding the outside diameter  D_o of a hollow shaft, the equation D_o^2 - DD_o - 0.25D^2 = 0 is used Solve for D_o if D = 3.625cm
    Last edited by danielwu; September 7th 2006 at 12:03 PM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by danielwu
    <br />
(1)----v(v + 2) = 15<br />
    v^2 + 2v = 15

    Now, x^2 + 2ax + a^2 = (x + a)^2

    Here we have 2 = 2a so a = 1. Thus add a^2 = 1 to both sides of the equation:
    v^2 + 2v + 1 = 15 + 1

    (v + 1)^2 = 16 Take the square root of both sides.

    v + 1 = \pm 4

    v = -1 \pm 4 = 3 or -5.

    (You should always be in the habit of checking your solutions to make sure they work. As it happens, they both do.)

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by danielwu
    (2)----5T^2 - 10T + 4 = 0
    [/tex]
    5T^2 - 10T = -4

    T^2 - 2T = -\frac{4}{5}

    (See previous post)
    -2 = 2a, so a = -1. Thus add a^2 = 1 to both sides.

    T^2 - 2T + 1 = -\frac{4}{5} + 1

    (T - 1)^2 = \frac{1}{5}

    T - 1 = \pm \sqrt{\frac{1}{5}} = \pm \frac{\sqrt{5}}{5}

    T = 1 \pm \frac{\sqrt{5}}{5}

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by danielwu
    (3)In machine design. in finding the outside diameter  D_o of a hollow shaft, the equation D_o^2 - DD_o - 0.25D^2 = 0 is used Solve for D_o if D = 3.625cm
    Same method. Get the constant term on the RHS of the equation, find out what "a" is, then add a^2 to both sides and go from there.

    -Dan
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by danielwu
    alright i have solve it.

    but here is another question which i also don't know how to do.
    can help me.

    ..[snip]
    Please post new unrelated questions in a new thread, it reduces confusion

    Thanks

    RonL

    (I will split this question out into a new thread)
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