Solve `x^2-4x-[x]=0` (where `[]` denotes the greatest integer function).

Explanation

To solve the equation \( x^2 - 4x - [x] = 0 \), where \([x]\) denotes the greatest integer function, we will analyze the equation over different intervals defined by the greatest integer function.

### Step 1: Understand the Greatest Integer Function
The greatest integer function \([x]\) gives the largest integer less than or equal to \(x\). For example:
- If \(x \in [0, 1)\), then \([x] = 0\).
- If \(x \in [1, 2)\), then \([x] = 1\).
- If \(x \in [2, 3)\), then \([x] = 2\), and so on.

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