Question

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.

Answer 1

Yes because both 169 and 9 are perfect squares. The square root of 169/9 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.

Explanation:

Answer 2

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.