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duty higher than -2

How can I expose this inequation in IR:

$$x-1+sqrt{{x^2}+2x+3}≥-2$$

I did this:

$$x-1+sqrt{{x^2}+2x+3}+2≥0$$

$$x+1+sqrt{{x^2}+2x+3}≥0$$

$$x+1+sqrt{{x^2}+2x+1+2}≥0$$

$$x+1+sqrt{{(x+1)^2}+2}≥0$$

$$if: x≥0 => x+1+sqrt{{(x+1)^2}+2}≥0$$

$$if: x<0 =>??$$ I do not know what I can do.

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