The number of solution of `x^2+|x-1|=1` is (a) `0` (b) `1` (c) `2` (d) `3`

Explanation

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

### Step 1: Case 1 - \( x \geq 1 \)
In this case, \( |x - 1| = x - 1 \). Therefore, the equation becomes:
\[ x^2 + (x - 1) = 1 \]
Simplifying this, we have:
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