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
We start with
Divide by :
Add to both sides in order to complete the square:
Complete the square:
Move to the other side:
Take the square root of both sides:
Finally, move the to the other side:
This is the quadratic formula, and we are done.
In some situations, it is preferable to use this variation of the quadratic formula: