Should I not answer my own questions?
What should I do if the given answers did not work for me, but I figured out a methodology that worked best for me/the_question. Should I answer my own question? (seems kind of weird).
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If your answer works then answer your own question. Even though it may feel a little weird, you are helping other people and that is what StackOverflow is all about!
If the answers given do not fit good for you ask the person to further explain their answer. If you still are not satisfied then absolutely yes and make sure you explain how you came to this answer and what other answers might have helped you figure out the best answer for you. Do not feel weird as it is your question and only you know what answer works the best. Answering your own questions shows that you are still doing research and not just letting everyone else do the work show that you follow through on ideas which might lead to more people giveing answers and a better overall idea.