Find the minimum value of
\[f(x) = \sqrt{5x^2 + 2x \sqrt{5} + 1} + x \sqrt{5},\]over all $x$ for which $f(x)$ is defined.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the minimum value of
\[f(x) = \sqrt{5x^2 + 2x \sqrt{5} + 1} + x \sqrt{5},\]over all $x$ for which $f(x)$ is defined.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-1
Find the minimum value of
\[f(x) = \sqrt{5x^2 + 2x \sqrt{5} + 1} + x \sqrt{5},\]over all $x$ for which $f(x)$ is defined.
train