The two solutions of the equation $x^2+bx+18=0$ are in the ratio of $2$ to $1$ for some values of $b.$ What is the largest possible value of $b?$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The two solutions of the equation $x^2+bx+18=0$ are in the ratio of $2$ to $1$ for some values of $b.$ What is the largest possible value of $b?$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
9
The two solutions of the equation $x^2+bx+18=0$ are in the ratio of $2$ to $1$ for some values of $b.$ What is the largest possible value of $b?$
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