Andy is solving a quadratic equation using completing the square. If a step in the process results in StartFraction 169 Over 9 E

Question

jekas

2 months ago

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Andy is solving a quadratic equation using completing the square. If a step in the process results in StartFraction 169 Over 9 E

ndFraction = (x – 6)2, could the original quadratic equation be solved by factoring? Explain your reasoning.

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-03-08T11:39:52+03:00

Answer:

Indeed, the equation is solvable by factoring. By applying the given equation, you can take the square root of both sides. Since both 169 and 9 are perfect squares, the left-hand side simplifies to plus or minus 13/3, producing rational results. Adding 6 to 13/3 yields a rational number while subtracting it does too. Thus, a quadratic equation is factorable if its solutions are rational.

Svet_ta [12.7K] · Answer 2 · 2026-03-08T11:40:39+03:00

Answer:

Yes, because both 169 and 9 are perfect squares, resulting in the square root of 169/9 being a rational number. Adding 6 to 13/3 also results in a rational outcome, and subtracting it gives a rational number as well. Therefore, if the solutions to a quadratic equation are rational, it's possible to factor the equation.

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