How many solutions are there for $x$ in the following equation: $$x^2 = -|x|.$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many solutions are there for $x$ in the following equation: $$x^2 = -|x|.$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
How many solutions are there for $x$ in the following equation: $$x^2 = -|x|.$$
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