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Math Help - quadratic equation

  1. #1
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    quadratic equation

    hi, i've got the question

    by completing the square, solve the following quadratic equation, giving your answer in surd form

    x^2 - x - 1 = 0

    my answer was x = 0.5 \pm \sqrt (0.75)

    but the books answer is x = 0.5 \pm \sqrt (5) frac(2)

    could someone please show me a step by step way of coming to this answer
    thanks

    ps that last bit was supposed to be the square root sign with the 5 to the right of it, then a division bar beneath them and a 2 underneath that, if someone could tell me how to write that properly that would be appreciated too
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  2. #2
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    Quote Originally Posted by mark View Post
    hi, i've got the question

    by completing the square, solve the following quadratic equation, giving your answer in surd form

    x^2 - x - 1 = 0

    my answer was x = 0.5 \pm \sqrt (0.75)

    but the books answer is x = 0.5 \pm \sqrt (5) frac(2)

    could someone please show me a step by step way of coming to this answer
    thanks

    ps that last bit was supposed to be the square root sign with the 5 to the right of it, then a division bar beneath them and a 2 underneath that, if someone could tell me how to write that properly that would be appreciated too
    x^2 - x -1 =0

    x^2 - x = 1

    (x-\frac{1}{2})^2 - \frac{1}{4} = 1

    You should be able to solve it from there. Also recall that \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} and also \sqrt{\frac{a}{c^2}} = \frac{\sqrt{a}}{c}
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  3. #3
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    Quote Originally Posted by mark View Post
    but the books answer is x = 0.5 \pm \sqrt (5) frac(2)


    ps that last bit was supposed to be the square root sign with the 5 to the right of it, then a division bar beneath them and a 2 underneath that, if someone could tell me how to write that properly that would be appreciated too
    You were close. You had

    [tex]x = 0.5 \pm \sqrt (5) frac(2)[/tex]

    and what you want is

    [tex]x = 0.5 \pm \frac{\sqrt{5}}{2}[/tex]

    which looks like

    x = 0.5 \pm \frac{\sqrt{5}}{2}

    Fractions are written with \frac{N}{D}, where N is the numerator and D is the denominator.

    You can always click on any LaTex output in a post and you will get a little popup window that shows the markup used to format it.
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  4. #4
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    i'm still not sure i understand, i'll show my method of figuring it out and hopefully someone will tell me where i went wrong with the equation x^2 - x - 1 = 0

    i started by putting it like this (x - 0.5)^2 - 0.75 = 0 because -0.5^2 is -0.25 and then you minus another .75 to get to the original -1 then you turn the equation into (x - 0.5)^2 = 0.75 then (x - 0.5) = \pm\sqrt{0.75} then x = 0.5 \pm \sqrt {0.75}
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  5. #5
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    Hi

    i started by putting it like this (x - 0.5)^2 - 1.25 = 0 because (-0.5)^2 is +0.25 and then you minus another 1.25
    to get to the original -1 then you turn the equation into (x - 0.5)^2 = 1.25 then (x - 0.5) = \pm\sqrt{1.25} then x = 0.5 \pm \sqrt {1.25}
    x = 0.5 \pm \sqrt {1.25} = \frac12 \pm \sqrt {\frac54} = \frac12 \pm \frac{\sqrt {5}}{2}
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  6. #6
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    ah i see i made a bit of a stupid mistake there, thanks
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