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Math Help - Quadratic Equation

  1. #1
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    Quadratic Equation

    I've been working on this equation, here's what I have so far:

    z^2-4z+26=0
    z^2-4z+4=30
    (z-2)^2=30
    z-2= +- Square root of 30
    ...
    And here I'm lost. Please help.
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  2. #2
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    Re: Quadratic Equation

    Quote Originally Posted by HellBunny View Post
    I've been working on this equation, here's what I have so far:
    z^2-4z+26=0
    z^2-4z+4=30
    (z-2)^2=30
    z-2= \pm \sqrt{30}
    Please use the correct LaTeX tags.
    [TEX]z-2= \pm \sqrt{30}[/TEX] gives z-2= \pm \sqrt{30}
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  3. #3
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    e^(i*pi)'s Avatar
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    Re: Quadratic Equation

    Quote Originally Posted by HellBunny View Post
    I've been working on this equation, here's what I have so far:

    z^2-4z+26=0
    z^2-4z+4=30
    (z-2)^2=30
    z-2= +- Square root of 30
    ...
    And here I'm lost. Please help.
    How did you get from the first line to the second? Your quadratic equation has two complex solutions since b^2-4ac<0
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  4. #4
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    Re: Quadratic Equation

    Okay ( to first poster )

    (Second poster)
    [1/2(-4)]^2
    Is how I got the input.
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Quadratic Equation

    Quote Originally Posted by HellBunny View Post
    I've been working on this equation, here's what I have so far:

    z^2-4z+26=0
    z^2-4z+4=30
    (z-2)^2=30
    z-2= +- Square root of 30
    ...
    And here I'm lost. Please help.
    This is not correct. It has to be:
    z^2-4z+26=0
    \Leftrigharrox (z^2-4z+4)+22=0
    \Leftrightarrow (z-2)^2=-22
    \Lefrightarrow z-2= \pm \sqrt{-22}
    \Leftrightarrow z=\pm \sqrt{-22} + 2

    Now, what's \sqrt{-22}?

    Note that D<0 therefore there're only complex roots, like we obtained.
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  6. #6
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    Re: Quadratic Equation

    Quote Originally Posted by HellBunny View Post
    Okay ( to first poster )

    (Second poster)
    [1/2(-4)]^2
    Is how I got the input.
    I still don't follow what you did to the value of "c".

    If you took 22 from both sides (which is what the LHS suggests) then you'd have -22 on the right (giving complex solutions)
    If you added 30 to both sides as implied then you'd have +56 on the left.


    Edit: too slow
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  7. #7
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    Re: Quadratic Equation

    It's fine ^. Thanks, that's the answer! Thank you all again for helping.
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