Positive integers $a$, $b$, and $c$ are all powers of $k$ for some positive integer $k$. It is known that the equation $ax^2-bx+c=0$ has exactly one real solution $r$, and this value $r$ is less than $100$. Compute the maximum possible value of $r$.

Let's think step by step and output the final answer within \boxed{}.
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