Quadratic formula
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The quadratic formula is used to simplify the process of solving a quadratic equation. It is in the following form:
- <math>x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}</math>
In order to be solved using this formula, a quadratic equation must be in the following format:
- <math>ax^2+bx+c=0\!</math>
You simply substitute <math>a</math>, <math>b</math>, and <math>c</math> into the formula.
You can prove that the formula is correct by substituting the formula in place of x in <math>ax^2+bx+c=0\!</math> and then gradually simplifying the rather complicated formula that results, step by step. Eventually, if all the simplifying steps are done correctly, it will simply to 0. Derivation of the formula is usually done via the method of completing the square.