The graph of the equation $y=ax^2+bx-6$ is completely below the $x$-axis. If $a^2=49$, what is the largest possible integral value of $b$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The graph of the equation $y=ax^2+bx-6$ is completely below the $x$-axis. If $a^2=49$, what is the largest possible integral value of $b$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
The graph of the equation $y=ax^2+bx-6$ is completely below the $x$-axis. If $a^2=49$, what is the largest possible integral value of $b$?
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