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How do I slove this quadratic equation?

  1. Mar 1, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm studying for the GMAT and the study materials do not include how to solve this equation. I need to know how to solve it without a calculator.

    2. Relevant equations

    If 2^x - 2^x-2 = 3(2^13), what is the value of X?

    3. The attempt at a solution

    The answer key says the the answer is 15. How did they come to this?
     
  2. jcsd
  3. Mar 1, 2012 #2

    tiny-tim

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    welcome to pf!

    hi kboynt1! welcome to pf! :smile:

    (try using the X2 button just above the Reply box :wink:)

    do you mean 2x - 2x-2 ?

    hint: what is 2x/2x-2 ? :wink:
     
  4. Mar 1, 2012 #3
    Would it be 2x-(x-2)?
     
  5. Mar 1, 2012 #4

    tiny-tim

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    sure would! :smile:

    and that equals … ? :wink:
     
  6. Mar 1, 2012 #5
    Holy Poop tim! my brain is about to explode... I don't know. :)
     
  7. Mar 1, 2012 #6

    tiny-tim

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    ok, when you're confused, do it one logical step at a time …

    what is x - (x - 2) ? :smile:
     
  8. Mar 1, 2012 #7
    wait... is it 22x-2?
     
  9. Mar 1, 2012 #8
    or is it... 2x/x-2?
     
  10. Mar 1, 2012 #9
    so we have to simplify the left side of the equation first?

    2x-2x-2=3(213)

    Then

    2x-(x-2)=3(213)

    Then...?
     
  11. Mar 1, 2012 #10
    is it just 2?

    so it's 22=4

    so

    4=3(213)? That doesn't seem right...
     
  12. Mar 1, 2012 #11

    tiny-tim

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    yes! :smile:

    now stop trying to do both side of the equation at once

    just do the LHS, and keep changing it until it matches the RHS

    you have 2x/2x-2 = 4

    so (2x - 2x-2)/2x-2 = … ? :smile:
     
  13. Mar 1, 2012 #12
    is it?

    2x-(x-2)-2x-2-(x-2)

    4-1=3
     
  14. Mar 1, 2012 #13

    tiny-tim

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    yup! :smile:

    so your LHS is now 3(2x-2), and your RHS is 3(213),

    soooo … ? :wink:
     
  15. Mar 1, 2012 #14
    3(2x-2)=3(213)

    divide by 3 on both sides

    2x-2=213

    add 2 to both the exponents

    2x=215

    x must equal 15.


    Okay... so I'm still unclear of how you got to 3(2x-2) on the LHS I know how we got the 3 but what were the thoughts behind that and how did we retain the (2x-2)

    THANK YOU BTW... Just a little more explanation/breakdown.
     
  16. Mar 1, 2012 #15

    tiny-tim

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    2x - 2x-2

    = 222x - 2 - 2x-2

    = (22 - 1)2x-2
     
  17. Mar 1, 2012 #16
    So what's the rule that governs the division that was done to obtain the 3 but retain the 2x-1

    Sorry I'm a bit dense on this subject...

    for example is the rule: xy-xz=((xy-xz)/xz)xz
     
  18. Mar 1, 2012 #17

    tiny-tim

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    the rule is AB - B = (A - 1)B
     
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