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.

Question

Mathematics

Paige Hayden

22 November, 17:23

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.

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Answers (2)

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Tony Wheeler · Answer 1

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.

Nigel Williams · Answer 2

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