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Math Help - [SOLVED] Completed Square Form

  1. #1
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    Cool [SOLVED] Completed Square Form

    I can't get the write answers for the following, can you please solve them step by step:

    Factorize this by using the completed square method

    12x^2+x-6


    Using the completed square form, find the least or greatest value of the following, and the value of x for which this occurs


    4+6x=-x^2

    Thanks!
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  2. #2
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    Talking

    Quote Originally Posted by unstopabl3 View Post
    I can't get the [right] answers for the following....
    Please reply showing your steps, so we can help you find any errors.

    Thank you!
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  3. #3
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    a)
    12x^2+x-6
    12(x^2+x/12)-6
    12{(x+1/24)^2+(1/24)(-1/24)}-6
    12{(x+1/24)^2-1/576}-6
    [tex]{12(x+1/24)^2+12(-1/576)}-6
    {12(x+1/24)^2-1/48}-6
    {12(x+1/24)^2-1/48-6(48/48)}
    {12(x+1/24)^2-289/48}

    From here onward I get stuck. Please tell me if I've made a mistake and solve from here onwards. Thanks.

    b)

    4+6x-x^2
    -1x^2+6x+4
    -{(x^2+6x)}+4
    -{(x+6)^2}+4
    -{(x+3)^2+3(-3)}+4
    -{(x+3)^2-9}+4
    -(x+3)^2+9+4
    -(x+3)^2+13

    when put x = 3
    then f(x) = 13

    The answer is correct but is this correct way to do it or is there another simpler method?

    Thanks!
    Last edited by unstopabl3; September 29th 2009 at 03:49 AM. Reason: The Latex keeps giving me errors
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  4. #4
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    Quote Originally Posted by unstopabl3 View Post

    12x^2+x-6

    4+6x=-x^2
    Instead of completing the square. Try using the quadratic formula


    where for the first equation: a=12 , b=1 , c=-6

    for the second equation: a=1 b=6, c=4
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  5. #5
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    Thanks but the question demands it that I solve it by using the completing square method

    Waiting for your solutions guys.
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  6. #6
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    Quote Originally Posted by unstopabl3 View Post
    a)
    12x^2+x-6
    12(x^2+x/12)-6
    12{(x+1/24)^2+(1/24)(-1/24)}-6
    12{(x+1/24)^2-1/576}-6
    [tex]{12(x+1/24)^2+12(-1/576)}-6
    {12(x+1/24)^2-1/48}-6
    {12(x+1/24)^2-1/48-6(48/48)}
    {12(x+1/24)^2-289/48}
    12((x+1/24)^2-289/576)
    12((x+1/24)^2-(17/24)^2) <<<<<<<<< difference of squares!
    12(x+1/24+17/24)(x+1/24-17/24))
    12(x+3/4)(x-2/3) <<<<<<<<< now split the factor 12 into 3 * 4 and put them into the appropriate bracket
    (4x+3)(3x-2)


    b)

    4+6x=-x^2 <<<<<<<<< according to the wording of the problem
    x^2+6x+4 = 0
    (x^2+6x+9-9)+4=0
    (x+3)^2-5=0
    (x+3)^2-(sqrt(5))^2=0 <<<<<<<<<<< difference of squares

    Factor the difference.
    Aproduct equals zero if one factor equals zero.
    Solve each equation for x.


    Thanks!
    ...
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