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Number of values of $$x$$ such that $$|x| + \sqrt{x} + [x] = x$$, where $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is
$$\sqrt{x}$$ is defined only for $$x \ge 0$$, and then $$|x| = x$$, so the equation becomes $$\sqrt{x} + [x] = 0$$. Both terms are non-negative, so both must be 0, which gives $$x = 0$$. There is exactly 1 value.
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