Given that \[x^2 + \lfloor x \rfloor = 75,\]find all possible values for $x.$  Enter all solutions, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Given that \[x^2 + \lfloor x \rfloor = 75,\]find all possible values for $x.$  Enter all solutions, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{67}, -\sqrt{85}
Given that \[x^2 + \lfloor x \rfloor = 75,\]find all possible values for $x.$  Enter all solutions, separated by commas.
train