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??????/
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]
or:
[tex](x+\frac{b}{2a}) =\pm\sqrt{(\frac{b}{2a})^2-\frac{c}{a}}[/tex]
or:
[tex]x =-\frac{b}{2a}\pm\sqrt{(\frac{b}{2a})^2-\frac{c}{a}}[/tex]
or:
[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]