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Math Help - Self-learner having trouble with quadratic equation

  1. #1
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    Self-learner having trouble with quadratic equation

    Hi. First of all - sincere apologies if this is in the wrong place. I have read the rules, but unfortunately don't really know all categories of mathematics, or what comes under which umbrella.

    Anyway, simple quadratic equations I don't find difficult.

    However, this problem is seriously getting to me. The exercise book I have bought claims the answer to be 0.2, but I simply cannot find out why. I thought QE were meant to have values, and this is just making me crazy.

    (x-1)^2 = x(x-3)

    I have expanded the brackets to find:

    X^2-2x+1 = X^2-3x

    But I have honestly no clue where to go from next. I have tried researching it, or finding other similar problems online but to no avail.

    Thanks in advance.
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  2. #2
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    e^(i*pi)'s Avatar
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    This is a linear equation rather than quadratic. You have x^2 on both sides and it will cancel.

    If you take x^2-3x from both sides you will get x^2-2x+1 - x^2+3x = 0 which simplifies to x+1=0

    It follows that x=-1 is the solution because (-1-1)^2 = -1(-1-3) \rightarrow 4 = 4 whereas x=0.2 gives (0.2-1)^2 = -0.2(0.2-3) \rightarrow 0.64 \neq 0.56



    edit: as a background you can have one solution to a quadratic equation (technically 2 equal roots). This happens when the discriminant \left(\Delta = b^2-4ac\right) is equal to 0.

    For example find the solution(s) to 4x^2-4x+1=0 (answer in spoiler)

    Spoiler:
    4x^2-4x+1 = (2x+1)^2 = 0 \rightarrow \: x = -\dfrac{1}{2}
    Last edited by e^(i*pi); October 12th 2010 at 12:24 PM. Reason: latex+see post
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  3. #3
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    Thanks very much. It's in the QE part of my workbook... and the answer is listed as 0.2. I had solved it as you did before, but just assumed that was too simple or something.

    I'll assume it's a misprint - thanks for your help.
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  4. #4
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    Quote Originally Posted by S1919 View Post
    (x-1)^2 = x(x-3)
    Looks like that equation contains a typo: should be (x - 1)^2 = x(x + 3) ?
    That would explain the .2 solution:
    x^2 - 2x + 1 = x^2 + 3x
    5x = 1
    x = 1/5 = .2
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