Quadratic formula
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.
Given the values , we can find all real and complex solutions to the quadratic equation.
Variation
In some situations, it is preferable to use this variation of the quadratic formula: