Andy is solving a quadratic equation using completing the square. If a step in the process results in StartFraction 169 Over 9 EndFraction = (x – 6)2, could the original quadratic equation be solved by factoring? Explain your reasoning.

Yes, the equation can be solved by factoring. Using the given equation, take the square root of both sides. Both 169 and 9 are perfect squares, so the left side becomes plus or minus 13/3, which is rational. Six plus 13/3 is a rational number, and 6 minus 13/3 is also a rational number. If the solutions of a quadratic equation are rational, then the equation is factorable.