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Math Help - need help understanding how to solve for x

  1. #1
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    need help understanding how to solve for x

    2x^2=1

    i divided by 2 to get x^2=1/2

    then to get x i took the radical \sqrt{x}=\sqrt{1}/\sqrt{2}

    but it doesn't make sense to me after that.

    then eventual answer is \sqrt{2}/2
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  2. #2
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    Quote Originally Posted by rasczak View Post
    2x^2=1

    i divided by 2 to get x^2=1/2

    then to get x i took the radical sqrtx=sqrt1/sqrt2

    but it doesn't make sense to me after that.
    Technically you did isolate the variable x by saying that

    x=1/2\,\sqrt {2}

    It is standard practice to eliminate the radical in the denominator. In this case, multiply both the top and the bottom by radical 2, and you should be fine.
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  3. #3
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    Quote Originally Posted by arcketer View Post
    Technically you did isolate the variable x by saying that

    x=1/2\,\sqrt {2}

    It is standard practice to eliminate the radical in the denominator. In this case, multiply both the top and the bottom by radical 2, and you should be fine.
    how did you come up with x=1/2\,\sqrt {2}?

    my math came up with x=1/\,\sqrt {2}.
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  4. #4
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    Quote Originally Posted by rasczak View Post
    how did you come up with x=1/2\,\sqrt {2}?

    my math came up with x=1/\,\sqrt {2}.
    Remember that when you have a fraction, you can multiply it by the number 1, and the value will be unchanged. This is obvious, right?

    In this case, we multiply the fraction by the square root of two, DIVIDED by the square root of two. Obviously, that is equal to one. Then, you just simplify.

    On the denominator, you have the root of 2 multiplied by the root of 2, which is 2. On the top you get the square root of two, which is simply

    x=1/2\,\sqrt {2}

    Let me know if this makes sense.

    EDIT: Also, obviously, I assume you know that the square root of 1 is 1.
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  5. #5
    Super Member Bacterius's Avatar
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    (sorry) Yes, arcketer, you found one solution but not the other :

    2x^2 = 1

    This is equivalent (obviously) to :

    x^2 = \frac{1}{2}

    Therefore, taking the square root yields :

    x = \sqrt{\frac{1}{2}} and x = - \sqrt{\frac{1}{2}} (the square of a number is equal to the square of its opposite!)

    Using properties of square roots, the solutions become :

    x = \frac{\sqrt{1}}{\sqrt{2}} and x = - \frac{\sqrt{1}}{\sqrt{2}}.

    Simplifying :

    x = \frac{1}{\sqrt{2}} and x = - \frac{1}{\sqrt{2}}.
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  6. #6
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    Yes I forgot the negative term when taking the square root, my mistake. However, 1 / root(2) is the same as root(2) / 2.
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  7. #7
    Super Member Bacterius's Avatar
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    Quote Originally Posted by arcketer View Post
    Yes I forgot the negative term when taking the square root, my mistake. However, 1 / root(2) is the same as root(2) / 2.
    Yes, I edited, my bad. Sometimes I take too quick decisions
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  8. #8
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    Quote Originally Posted by Bacterius View Post
    Yes, I edited, my bad. Sometimes I take too quick decisions
    No worries, mate
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  9. #9
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    Quote Originally Posted by arcketer View Post
    Yes I forgot the negative term when taking the square root, my mistake. However, 1 / root(2) is the same as root(2) / 2.
    You will NEVER "[forget] the negative" if you use a procedure that makes you look at it.

    2x^{2} = 1

    2x^{2} - 1 = 0

    (\sqrt{2}x+1)(\sqrt{2}x-1) = 0

    How will you miss either solution?

    There is a reason why you studied all that factoring. You were just stuck with integers and rational numbers.
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  10. #10
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    Quote Originally Posted by arcketer View Post
    Remember that when you have a fraction, you can multiply it by the number 1, and the value will be unchanged. This is obvious, right?

    In this case, we multiply the fraction by the square root of two, DIVIDED by the square root of two. Obviously, that is equal to one. Then, you just simplify.

    On the denominator, you have the root of 2 multiplied by the root of 2, which is 2. On the top you get the square root of two, which is simply

    x=1/2\,\sqrt {2}

    Let me know if this makes sense.

    EDIT: Also, obviously, I assume you know that the square root of 1 is 1.
    unfortunately, a lot of this has left my brain. i haven't touched this material in fifteen years. I just started school this semester and i wasn't allowed to retake algebra ( passed it), so i took trig. I pretty far behind right now, but slowly getting back up to speed. I just hope i can catch up before the semester ends.
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