Question

ndy 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 1

If you use completing the square and ended up with (x-6)^2, it means it is a perfect square to start off with. That will mean that it can actually be solved by factoring.

x^2 -12x + 36 = (x-6)^2

Answer 2

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.