Solve `|x|= x^2-1`

Explanation

To solve the equation \( |x| = x^2 - 1 \), we need to consider two cases based on the definition of the absolute value function.

### Step 1: Set up the cases based on the absolute value
The absolute value function \( |x| \) can be defined as:
- \( |x| = x \) when \( x \geq 0 \)
- \( |x| = -x \) when \( x < 0 \)

### Step 2: Case 1: \( x \geq 0 \)
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