Compute the smallest real number $x$ which satisfies the equation \[\sqrt{x^2 - 2x + 2} + \sqrt{-x^2 + 6x - 2} = 2\sqrt{x}.\]
Question:
Compute the smallest real number $x$ which satisfies the equation \[\sqrt{x^2 - 2x + 2} + \sqrt{-x^2 + 6x - 2} = 2\sqrt{x}.\]
Answer:
Let's think step by step.

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