Why can ALL quadratic equations be solved by the quadratic formula?

Question

In algebra, all quadratic problems can be solved by using the quadratic formula. I read a couple of books, and they told me only **HOW** and **WHEN** to use this formula, but they don't tell me **WHY** I can use it. I have tried to figure it out by proving these two equations are equal, but I can't.Why can I use $x = \\dfrac{-b\\pm \\sqrt{b^{2} - 4 ac}}{2a}$ to solve all quadratic equations?

Answer 1

The Quadratic Formula is derived by completing the square on the most general quadratic polynomial:

ax² + bx + c = 0.

Since it is derived from the most general quadratic it can be used on all quadratics - although sometimes it need not be.