Find the minimum possible value of
\[\sqrt{58 - 42x} + \sqrt{149 - 140 \sqrt{1 - x^2}}\]where $-1 \le x \le 1.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the minimum possible value of
\[\sqrt{58 - 42x} + \sqrt{149 - 140 \sqrt{1 - x^2}}\]where $-1 \le x \le 1.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{109}
Find the minimum possible value of
\[\sqrt{58 - 42x} + \sqrt{149 - 140 \sqrt{1 - x^2}}\]where $-1 \le x \le 1.$
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