Difference between revisions of "Quadratic formula"
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Let the quadratic be in the form <math>ax^2+bx+c=0</math>. | Let the quadratic be in the form <math>ax^2+bx+c=0</math>. | ||
− | Moving | + | Moving <math>c</math> to the other side, we obtain |
<math>ax^2+bx=-c</math> | <math>ax^2+bx=-c</math> |
Revision as of 12:05, 24 February 2021
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 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: