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:
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 .