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Math Help - Solve for x...

  1. #1
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    Solve for x...

    Alright, I just got some ridiculously long five page answer that ended up with imaginary numbers as the answer.

    I think the problem is a bit more simple than what I used that's usually a dependable program to figure out an answer...

     \sqrt{x^2-4x+9}-x=-1
     \sqrt{x^2-4x+9}-x+x=-1+x
     \sqrt{x^2-4x+9}=0

    Get rid of the square root sign and voila...

    x-2+3=0
    x+1=0
    x-1=0-1
    x=-1

    Which is the correct answer. Was my method unorthodox or a coincidence or what?

    EDIT: This is not actually the right answer...the answer is x=4?

    Someone help?
    Last edited by A Beautiful Mind; July 16th 2009 at 11:04 AM.
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  2. #2
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    Quote Originally Posted by A Beautiful Mind View Post
    Alright, I just got some ridiculously long five page answer that ended up with imaginary numbers as the answer.

    I think the problem is a bit more simple than what I used that's usually a dependable program to figure out an answer...

     \sqrt{x^2-4x+9-x}=-1
     \sqrt{x^2-4x+9-x+x}=-1+x
     \sqrt{x^2-4x+9}=0

    Get rid of the square root sign and voila...

    x-2+3=0
    x+1=0
    x-1=0-1
    x=-1

    Which is the correct answer. Was my method unorthodox or a coincidence or what?

    EDIT: This is not actually the right answer...the answer is x=4?

    Someone help?
    please state the original problem from the beginning.
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  3. #3
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    The original problem is at the top of the first post.
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  4. #4
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    is that last x supposed to be under the radical?

    in other words, is the equation supposed to be

    \sqrt{x^2-4x+9} - x = -1

    because, as you have it written, \sqrt{x^2-4x+9-x} = -1 has no solution.
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  5. #5
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    I just checked and no, the x is not under the radical. Sorry about that, I thought the latex stuff just covered the first 3 but I guess not.
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  6. #6
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    \sqrt{x^2-4x+9} - x = -1

    \sqrt{x^2-4x+9} =  x - 1

    square both sides ...

    x^2 - 4x + 9 = (x-1)^2

    x^2 - 4x + 9 = x^2 - 2x + 1<br />

    combine like terms ...

    8 = 2x

    x = 4

    check the solution in the original equation ...

    \sqrt{4^2-4(4)+9} - 4 =

    \sqrt{16-16+9} - 4 =

    3 - 4 = -1

    checks good.
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