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Homework Help: Solve y explicitly

  1. May 8, 2010 #1
    1. Solve for y explicitly , x^2-4xy+4y^2+x-12y-10=0



    2. Relevant equations



    3. I reduced it to (x-2y)^2=-2x+12y+10 But I have no idea how to continue.
     
  2. jcsd
  3. May 8, 2010 #2

    Mark44

    Staff: Mentor


    Your equation is quadratic in y. Rewrite it as 4y^2 + (stuff)y + (other stuff) = 0, and use the quadratic formula.
     
  4. May 8, 2010 #3
    Even so I cant solve for y. Can you put a step by step explanation?
     
  5. May 8, 2010 #4
    The closest I get is (y-x)^2-3y=(3x^2-x+10)/4, how can i proceed?
     
  6. May 8, 2010 #5
    It is forbidden on these forums to post step-by-step solutions to a posted problem.
     
  7. May 8, 2010 #6
    sorry, I am new, but can you explain what do I do after, (y-x)^2-3y=(3x^2-x+10)/4?
     
  8. May 8, 2010 #7

    gabbagabbahey

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    Start by expanding (y-x)^2...then collect terms in powers of y.
     
  9. May 8, 2010 #8
    From there, I get y^2-2xy-x^2-3y=(3x^2-x+10)/4, I guess I could complete the square on the left side but I wouldn't really get anywhere I think.
     
  10. May 8, 2010 #9

    gabbagabbahey

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    When I say collect terms in powers of y, I mean write -2xy-3y as -(2x+3)y...so you have y^2-(2x+3)y-x^2=(3x^2-x+10)/4...subtract (3x^2-x+10)/4 from both sides of your equation and you can then use the quadratic equation to solve for y in terms of x.
     
  11. May 8, 2010 #10
    So would my -x^2-((3x^2-x+10)/4) be considered as my "C" value in my quadratic.
     
  12. May 8, 2010 #11

    gabbagabbahey

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  13. May 8, 2010 #12
    So... why wouldn't we just start with:
    x^2-4xy+4y^2+x-12y-10=0
    (4)y^2 + (-4x-12)y +(x^2 + x -10) = 0
    a, b, c....
    instead of completing - then UNcompleting - the square???
     
  14. May 8, 2010 #13
    Lol, Yes i have noticed that and yes it works!. Thanks for your help guys. I just went back to my original equation and did quadratic formula =D.
     
  15. May 8, 2010 #14
    Cool man. Hope to help more (or some :wink:) in the future!
     
  16. May 9, 2010 #15

    Mark44

    Staff: Mentor

    Which is what I was talking about in post #2...
     
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