Andy is solving a quadratic equation using completing the square. If a step in the process results in = (x – 6)2, could the original quadratic equation be solved by factoring? Explain your reasoning.

Answer:

Yes, the original equation can be solved by factoring. Taking the square root of both sides of (x – 6)² = 169/9 gives x – 6 = ±13/3 because 169 and 9 are perfect squares. This results in rational solutions for x (x = 31/3 and x = 5/3). Since the solutions are rational numbers, the original quadratic expression is factorable.