# Difference between revisions of "Quadratic formula"

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− | The '''quadratic formula''' is a general [[expression]] for the [[solution]]s to a [[quadratic equation]]. | + | The '''quadratic formula''' is a general [[expression]] for the [[solution]]s 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. |

## Revision as of 19:37, 21 September 2007

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

.

Factoring 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: