The quadratic formula is a general expression for the solutions to a quadratic equation. It is used when other methods, such as completing the square, factoring, and square root property do not work or are too tedious.
General Solution For A Quadratic by Completing the Square
Let the quadratic be in the form .
Moving c to the other side, we obtain
Dividing by and adding to both sides yields
Completing the square on the LHS gives
As described above, an equation in this form can be solved, yielding
This formula is also called the quadratic formula.
In some situations, it is preferable to use this variation of the quadratic formula: