Compute the smallest real number $x$ which satisfies the equation \[\sqrt{x^2 - 2x + 2} + \sqrt{-x^2 + 6x - 2} = 2\sqrt{x}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute the smallest real number $x$ which satisfies the equation \[\sqrt{x^2 - 2x + 2} + \sqrt{-x^2 + 6x - 2} = 2\sqrt{x}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3-\sqrt7
Compute the smallest real number $x$ which satisfies the equation \[\sqrt{x^2 - 2x + 2} + \sqrt{-x^2 + 6x - 2} = 2\sqrt{x}.\]
train