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Math Help - Algebra: Solving for X (Data Sufficiency)

  1. #1
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    Algebra: Solving for X (Data Sufficiency)

    Hi All,
    Quick one on approach...

    Question: What is a value of x?

    (1) x^2 - 6 = -x
    (2) x^2 = 4

    This is how I tackled it...
    (1) x^2 -x = 6
    x = 6
    (2) x^2 = 4
    x = 6

    So my answer would be that both (1) and (2) are sufficient to answer this question.

    But no, the answer is.......

    (1) x^2 - x - 6 = 0
    x - 6 = 0
    (x + 3)(x - 2) so x could be 3 or -2

    (2) x^2 = 4
    x^2 + 4 = 0
    (x + 2)(x - 2)

    Common across both is -2 so the answer would be a combination of 1 and 2.

    My question is how does one know that they should set the equations equal to 0. Is it because the term 'solve' is used instead of.. 'What is x?'

    Also I would assume that if either of the above solved to a perfect square that would be the answer?

    Thanks in Advance,
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  2. #2
    MHF Contributor harish21's Avatar
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    You are finding the unknown, which is x.

    your approach to solving the problems is wrong.

    x^2-6=-x

    add 'x' on both sides of the equation, and you'll have:

    x^2+x-6=0. Now solve for x using the appropriate approach.

    and x^2=4 means x^2-4=0
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  3. #3
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    Quote Originally Posted by harish21 View Post
    You are finding the unknown, which is x.

    your approach to solving the problems is wrong.

    x^2-6=-x

    add 'x' on both sides of the equation, and you'll have:

    x^2+x-6=0. Now solve for x using the appropriate approach.

    and x^2=4 means x^2-4=0
    Thanks for the response. I know I'm wrong and I the answer makes sense once it is set to 0. My question was how I know to set the equation to 0 by the question; given that in instances where you are asked for x, when left with x^2 = 4. The natural tendency would be to say x = 2.
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  4. #4
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    Quote Originally Posted by dumluck View Post
    (1) x^2 - 6 = -x
    (2) x^2 = 4
    (1)x^2 + x - 6 = 0
    (2)X^2 + 0 - 4 = 0
    Subtract (2) from (1):
    0 + x - 2 = 0
    x = 2
    Roger!
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  5. #5
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    Quote Originally Posted by dumluck View Post
    (1) x^2 - 6 = -x
    (2) x^2 = 4
    Add x to both sides of x^2- 6= -x: x^2- 6+ x= -x+ x so x^2+ x- 6= 0.

    Subtract 4 from both side of x^2= 4: x^2- 4= 4- 4 so x^2- 4= 0.
    [/QUOTE]
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