Of course! first of all, we know that `f(x) = sin(x) + x^2` is a continuous, differentiable function, with its derivative being `f'(x) = cos(x) + 2*x`.
After this, we make a guess on where the root could potentially be, one trivial root is at 0 since `f(0) = sin(0) + 0^2 = 0`, we make a guess that a second root is at `x_0 = -1` since `f(-1) = sin(-1) + (-1)^2 ≈ 0.16` (a value close to zero). And then from there we can start incrementally improving this guess using the formula `x_n+1 = x_n - f(x_n) / f'(x_n)`
So with this we can start by calculating x_1, and then x_2 and so on
1. `x_1 = x_0 + f(x_0) / f'(x_0) = -1 - (sin(-1) + 1) / (cos(-1) - 2) ≈ -0.891396`
2. `x_2 = x_1 + f(x_1) / f(x_1) ≈ -0.8769848`
3. `x_3 = x_2 + f(x_2) / f(x_2) ≈ -0.8767263`
4. `x_4 = x_3 + f(x_3) / f(x_3) ≈ -0.8767262` and here we can stop since the first five digits did not change from the previous answer, meaning that we have reached five digits of precision

This gives us the answer of `x = -0.87672` as the second root.
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