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Find quadratic equation

  1. Sep 21, 2016 #1
    1. The problem statement, all variables and given/known data
    X^2-yx+y^2-7=0

    2. Relevant equations

    -b +- sqrt(b^2-4ac)/2a

    3. The attempt at a solution
    Trying to complete the square with two variables
    (x^2-yx)+(y^2)=7

    (X^2-yx+y/2)+y^2=7
    Where else from here. I'm just having problems because of the y variable
     
  2. jcsd
  3. Sep 21, 2016 #2

    Mark44

    Staff: Mentor

    What's the complete problem statement? IOW, what are you supposed to do here?
     
  4. Sep 21, 2016 #3
    The original equation was a differential equation
    (2x-y)dx+(2y-X)dy= 0
    Which I solved and got
    X^2-yx+y^2=7

    It took the form of
    M(X,y)dx+N(X,y)=0

    M(partial y)= N(partial X)

    So it had an exact solution
    I then continued the rest of the steps and got my final answer but it needs to be in terms of y.

    The final answer is

    Y=[x+sqrt(28-3x^2)]/2, |x|<sqrt(28/3)

    I'm trying to transform my answer into their final answer.
     
  5. Sep 21, 2016 #4
    I need help completing the squares so that I can use the quadratic equation to solve for y.
     
  6. Sep 21, 2016 #5

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You need y as function of x. So write y2-yx+x2-7 in form (y-x/2)2+f(x)
     
  7. Sep 21, 2016 #6

    Mark44

    Staff: Mentor

    @Ashley1nOnly, your first post should have started like this:

    One other thing -- what you wrote above would be interpreted by most as
    $$-b \pm \frac{\sqrt{b^2 - 4ac}}{2} a$$
     
  8. Sep 21, 2016 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You have an equation of the form ##y^2 + b y + c = 0##, with appropriate ##b## and ##c##. The solution forms
    $$y_1 = \frac{-b + \sqrt{b^2 - 4 c}}{2} , \; y_2 = \frac{-b - \sqrt{b^2 - 4 c}}{2} $$
    will give you the answer. It does not matter if ##b,c## are numerical constants, or if they are 1000-page formulas containing 500 other variables; as long as they do not contain ##y##, the quadratic solution formula holds and you are good to go.
     
    Last edited: Sep 21, 2016
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