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

Question

Ilia_Sergeevich [38]

3 years ago

14

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:

aleksklad [387] · Answer 1 · 2022-03-16T03:01:12+03:00

Answer:

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.

bagirrra123 [75] · Answer 2 · 2022-03-16T04:30:11+03:00

Answer:

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.

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