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9-39.

Solve the following quadratic equations using any method.

Example 1: Solve for using the Zero Product Property.

Solution: First, factor the quadratic so it is written as a product: . (If factoring is not possible, one of the other methods of solving must be used.)  The Zero Product Property states that if the product of two terms is , then at least one of the factors must be .  Thus,  or . Solving these equations for reveals that or that .

Example 2: Solve for using the Quadratic Formula.

Solution: This method works for any quadratic.  First, identify , and  equals the number of -terms, equals the number of -terms, and equals the constant. For , and .  Substitute the values of , and into the Quadratic Formula and evaluate the expression twice: once with addition and once with subtraction. Examine this method below:

  

   

or

      

   

      

Example 3: Solve  by completing the square.

Solution: This method works most efficiently when the coefficient of  is .  Rewrite the equation as .  Rewrite the left side as an incomplete square:  

+

    +    

Complete the square and rewrite as
 or 

Take the square root of both sides, .  Solving for reveals that  or .