How was the quadratic formula found and proven? Possible Duplicate:
  Why can ALL quadratic equations be solved by the quadratic formula?
  History of Quadratic Formula  




How was the quadratic formula $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ found and proven?
I don't know for sure, but I imagine it was first found by thinking about rearranging squares and rectangles, as in the following image:
by completing the square. $a\neq 0$,  $ax^2+bx+c=a\left(x^2+\dfrac{b}{a}x+\dfrac{c}{a}\right)=\cdots$