Example 4:          Solve:  x² – 9 = 0

 

Solution:               

Whenever an equation is missing the x-term, it is easier to NOT use the quadratic formula.  In this problem we can factor the left side as the difference of squares and then use the zero-product property to solve:

                             (x – 3)(x + 3) = 0

                             x – 3 = 0 -->   x = 3

                             x + 3 = 0  -->  x = –3

We could also rewrite this equation as x² = 9 and then take the square roots of both sides, but remember that there are two square roots of any positive number – one positive and one negative:

                             x² = 9  -->  x  =  3  and  x  =  –3

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