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Math Help - Completing the square and simplifying.

  1. #1
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    Completing the square and simplifying.

    Can you please help me and solve these questions by completing the square (keeping the fractions in fraction-form rather than changing them to decimals) and can you please show your work, so I can see what you're
    doing? Also, can you then simplify the fractions? If you cannot do all of them, can you do at least one? PLEASE. I'm really confused.

    1.) 2/3^2 - 2x - 3 = 0
    2.) 1/4n^2 + n = - 1/8
    3.) 3m^2 + 8m + 8 = 0
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  2. #2
    Member elninio's Avatar
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    Use the quatratic formula.

    If a+bx+cx^2

    Then:
    http://trevorpythag.files.wordpress..../02/qdrtc2.gif
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  3. #3
    Senior Member pacman's Avatar
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    1.) 2/3^2 - 2x - 3 = 0
    2.) 1/4n^2 + n = - 1/8
    3.) 3m^2 + 8m + 8 =
    0


    3) Solution: 3m^2 + 8m + 8 = 0,

    3m^2 + 8m = -8

    m^2 + (8/3)m = -8/3, complete the square,

    m^2 + (8/3)m + ((8/3)/2)^2 = -8/3 + ((8/3)/2)^2,

    m^2 + (8/3)m + (8/6)^2 = -8/3 + (8/6)^2,

    m^2 + (8/3)m + (4/3)^2 = -8/3 + (4/3)^2,

    (m + 4/3)^2 = -8/3 + 16/9,

    (m + 4/3)^2 = (-24 + 16)/9,

    (m + 4/3)^2 = -8/9, take square root of BS,

    m + 4/3 = (+/-) sqrt (-8/9),

    m = - 4/3 (+/-) sqrt (-8/9), we HAVE two roots

    NOTE: sqrt (-8/9) = sqrt ((-2)(4)/9) = sqrt ((-2)(2^2)/3^2) = sqrt ((-2)(2/3)^2) = 2/3 sqrt (-2)

    m1 = -1.333 + 0.943 i

    m2 = -1.333 - 0.943 i





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