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Can Anyone Understand this?

  1. Mar 14, 2010 #1
    Can Anyone Understand this???

    See the attachment///
    Can Anyone Understand this???
    I mean what metod has he followed to solve this equation for x in terms of y , does someone have any method to solve it other than the quadratic formula??????/

    Attached Files:

  2. jcsd
  3. Mar 14, 2010 #2


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    Re: Can Anyone Understand this???

    It's called "completing the square", and it's where the quadratic formula comes from. Remember, if I have:
    [tex]x^2+2ax + a^2 = 0[/tex] , I can write it as
    [tex](x+a)^2 = 0[/tex] .
    So if I have
    [tex]ax^2+bx+c = 0[/tex]
    I can write it as:
    [tex]x^2+\frac{b}{a}x+(\frac{b}{2a})^2 =(\frac{b}{2a})^2-\frac{c}{a}[/tex]
    where I have added [tex](\frac{b}{2a})^2[/tex] to both sides. This is also:
    [tex](x+\frac{b}{2a})^2 = (\frac{b}{2a})^2-\frac{c}{a}[/tex]
    [tex](x+\frac{b}{2a}) =\pm\sqrt{(\frac{b}{2a})^2-\frac{c}{a}}[/tex]
    [tex]x =-\frac{b}{2a}\pm\sqrt{(\frac{b}{2a})^2-\frac{c}{a}}[/tex]
    [tex]x =\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

    This is what they have done, but with [tex]\frac{7y+13}{24}[/tex] playing the role of [tex]\frac{b}{2a}[/tex]
  4. Mar 14, 2010 #3
    Re: Can Anyone Understand this???

    Thanks friend
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