Are you smarter than an 8th grader? #2

Number Theory Level 4

Given that \(a\) has a remainder of \(6\) and \(b\) has a remainder of \(1\) when divided by \(14\), what is the remainder of \(x\) when divided by \(14\), given \(x\) is an integer solution to \(x^{2}-2ax+b=0\)

This problem is part of the question set Mathematics in Anime. It appears in the anime Puella Magi Madoka Magica. Students attending the Math class are only \(14\) years old, yet they are expected to solve this question on the spot!

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