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Solve for x

  1. Jan 17, 2005 #1
    For some reason i can't solve for x:


    I have M value: (5.98)(10)^24

    d is: (3.84)(10)^5
  2. jcsd
  3. Jan 17, 2005 #2
    show your work
  4. Jan 17, 2005 #3
    i started with cross multiplying:



    then i divided both sides by the left side and crossed out M.

    From there I don't know what to do
  5. Jan 17, 2005 #4


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    After you divided both sides by M and then divided both sides by .012, you should have wound up with:


    Split the right side up into three fractions:


    Substitute in your value for d. That should leave you with something you can work with.
  6. Jan 18, 2005 #5


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    Actually, I wouldn't divide both sides by 0.012, just because I don't like fractions!

    0.012x2= d2- 2dx+ x2 is the same as (subtract 0.012x2 from both sides)
    0.988x2- 2dx+ d2= 0.

    With d= 3.85 x 105, d2= 1.48225 x 1011 so your equation is
    0.988x2- (7.7 x 105)x+ 1.48225 x 1011= 0.

    You can solve that with the quadratic formula.
  7. Jan 18, 2005 #6
    does d in this case stand for difference like in calculus or is it just any other variable?
  8. Jan 18, 2005 #7


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    By,the looks of it,it's a dimensionful number...


    PS.Got it,it's the mean distance Earth-Moon and M is the Earth's mass... :tongue2: :approve: And it's in Km.
  9. Jan 18, 2005 #8
    couldnt you first divde M on both sides and then find the square root??

    as in

    [tex] \frac{0.012M}{(d-x)^2} = \frac{M}{x^2} [/tex]
    which then gives

    [tex] \frac{0.012}{(d-x)^2} = \frac{1}{x^2} [/tex]

    and then find the square rooton both sides

    [tex] \frac{\sqrt{0.012}}{d-x} = \frac{1}{x} [/tex]

    then cross multiply and solve without need for a quadratic??
  10. Jan 18, 2005 #9


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    I'm sorry,but it doesn't work that way.You need to consider the modulus when extracting sqrt,which would complicate the problem...

  11. Jan 18, 2005 #10
    see i think it's this,

    cross multiply,


    x/(d-x)={1/0.012}^1/2 (that is sq root)


    dividing the numerator & denominator by x

    1/{(d/x) - 1}=9.13

    {(d/x) - 1}=1/9.13


    since,d is: (3.84)(10)^5,we have

    =345,945.95 units
  12. Jan 18, 2005 #11


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    THAT IS DEVIOUS...U should have a [tex] \pm [/tex] sign... :grumpy:

  13. Jan 18, 2005 #12
    if its correct please tell me. :smile:
  14. Jan 18, 2005 #13


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    I thought i put in a very obvious way... :tongue2: It's wrong.By inappropriately extracting square root,u lost one (possibly viable) solution.

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