How did you solve the equation?

7 Comments

  • Stephanie Frost - 14 years ago

    I enjoyed this exercise. I treated it as a journal and recorded everything:

    x^2 + 2x + 1 = x^2
    -Okay, let's copy this down on paper. It has been many years since I've actually worked on an algebra problem.
    -I remember something about the equals sign. Right. Whatever operation you perform on one side, you must do exactly the same on the other side.
    - I also remember that you are supposed to make one side zero.
    - I don't know what the overall goal is or what this representation is for. Oh, I guess you are supposed to find the value of x. I recall doing this repetitively, but I wish I understood a larger picture of why I would ever want to know x, and what x might be symbolizing.
    x^2 + 2x +1 -x^2 = 0
    -cancel out the two x^2s
    2x + 1 = 0
    - Then subtract the 1 on both sides because we want an 'x' on one side by itself
    2x = -1
    - Then divide by 2 on both sides because this will isolate x.
    x = -1/2
    - Okay, so what part of my written process conforms to the rubric put forward in the original question?

    (and then I clicked my answer in the poll and came here to type this!)

  • Sudip paul - 14 years ago

    My thinking process has not been included in the options. It is 12. Seeing the equation I promptly cancelled x^2 from both sides to get x=-1/2. Then I observed that both sides are perfect squares and for a moment was bewildered to think that this process gives two solutions where there is only one possible. Then I found that one square root gives x+1=x and hence has to be discarded.

  • Elad - 14 years ago

    For me it was the same as for E Coffin. (Thus I voted 21 but that doesn't really represent what happened. It's more like expecting 2 before reading the equation, and then realizing 1 is possible)

  • Robin Evans - 14 years ago

    I think my thought process was heavily influenced by the expectation of a 'trick' question...

    First I saw the familiar quadratic on the left, then noticed the right hand side, and thought of 1.

    This was followed by thinking very carefully about why this must be wrong, and how I would be made to feel a fool later on!

    An interesting experiment nonetheless.

  • E Coffin - 14 years ago

    I was a bit premature in starting to solve the problem: I was plotting out the approach before I'd finished reading the equation. When I saw the x^2 I assumed it was in canonical form (out of the corner of my eye I saw no superscripts in the next few terms), when I saw the 2x I became more sure, as soon as I saw the 1, I factored it to (x+1)^2. Then I saw the x^2 on the RHS. At that point I realized approach #1 was the right one.

  • jocloud31 - 14 years ago

    I actually took notes of my process while I was doing it, from start to finish. I expected to run into issues, since I'm pretty terrible at algebra, but it would seem the problem was straight forward. Unless I still did the algebra wrong, then I guess it wasn't.

    subtract x^2 from both sides
    leaves 2x + 1 = 0
    subtract 1 from both sides
    leaves 2x = -1
    divide by 2
    leaves x = -1/2

  • RL - 14 years ago

    The very first thought I had was that the answer must be 0, but then I went quickly to solution 1. I suppose my initial reaction was as it was because I'm always hesitant to cancel out squares (or whatever the highest power is) out of concern for losing some information. Dumb, I know, but I'm doing my part to help the study through full disclosure of faulty thought processes :-)

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