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Absolute value question

  1. Jan 5, 2008 #1
    1. The problem statement, all variables and given/known data

    25|x| = x^2 + 144



    2. Relevant equations

    none

    3. The attempt at a solution

    okay well, i'm not quite sure what to do, do i try to isolate the |x|? and then break it up into a postive and negative?

    |x| = (x^2 + 144)/25 ?

    but from here i become lost.....
     
  2. jcsd
  3. Jan 5, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Why not do what you just said? You have "isolated" |x|, now break it into positive and negative parts.

    If [itex]x\ge 0[/itex] then |x|= x so the equation becomes [itex]x= (x^2+ 144)/25[/itex] or [itex]25x= x^2+ 144[/itex]. Solve that quadratic equation. Remember that only [itex]x\ge 0[/itex] are valid solutions.

    If x< 0, then |x|= -x so the equation becomes [itex]-x= (x^2+ 144)/25[/itex] or [itex]-25x= x^2+ 144[/itex]. Solve that quadratic equation. Remember that only x< 0 are valid solutions.

    You might notice that it is easier to first break into two cases and then solve for x.
     
  4. Jan 5, 2008 #3
    okay so should my answer be x = +/- 16, +/- 9?
     
  5. Jan 5, 2008 #4

    Gib Z

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    Homework Helper

    It's quite easy to check yourself =P Especially when checking one of the positive solutions gets rid of the negative counterpart as well.
     
  6. Jan 5, 2008 #5
    k thx
     
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