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Math Help - Completing the square confusing me

  1. #1
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    Completing the square confusing me

    I have a question that requires me to solve by completing the square but leave the answers in SURD form:

    I have got as far as the following:

    x^2+8x+10=0
    x^2+8x+10=(x-4)^2-4^2+10
    (x-4)^2-16+10
    (x-4)^2-6=0
    (x-4)^2=6
    x-4=√6 or -√6
    x=4√6 or -4√6

    Now I think this is wrong I just don't know what steps are missing or at what point i have made a mistake?

    Any help is appreciated.

    Thanks in advance.
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  2. #2
    A Plied Mathematician
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    From second-to-last step to last step, there is an algebra error.
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  3. #3
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    Thanks for the quick reply, much appreciated. that's where I thought the error was but I thought you square root each side.

    Again many thanks.
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  4. #4
    A Plied Mathematician
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    Nope, everything's good up to that last step. What should you be doing there?
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  5. #5
    A Plied Mathematician
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    Actually, I'm wrong. Look here:

    x^{2}+8x+10=0
    x^{2}+8x+16-16+10=0
    (x+4)^{2}-6=0
    .
    .
    .
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  6. #6
    Super Member bigwave's Avatar
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     <br />
x^2+8x+10=0<br />
     <br />
x^2+8x+10+6 = 6 \Rightarrow (x+4)^2-6=0<br />
     <br />
x = -4\pm\sqrt{6}<br />

    EDIT: to late again...
    Last edited by bigwave; June 8th 2010 at 01:25 PM. Reason: latex
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  7. #7
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    Thanks a lot!
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  8. #8
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    Another way of going about it

    Fortunately your starting equation is in standard form so just follow these steps:

    1) Move the ten to the other side to get:

    x^2 + 8x = -10

    2) Take 1/2 of the number in the 8x term, square it, then add the result to both sides which yields:

    x^2 + 8x + 16 = -10 + 16 = 6

    3) Now factor out the left-hand side to get:

    (x + 4)^2 = 6

    Can you proceed from here on?
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