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Solving Quadratics by the Quadratic Formula

The following represents any quadratic equation:




This can be solved using the completing the square method to produce a formula that can then be applied to all quadratic equations.

Example 1: Solve , for x by using the completing the square method.




Get the coefficient of the squared term to be 1.




Isolate the variable terms.




Complete the square.




Apply the square root property.




This last result is referred to as the quadratic formula. Remember, the quadratic formula can be used to solve all quadratic equations.




Example 2: Solve by applying the quadratic formula.




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