algebraic manipulation - How to extract expression from ConditionalExpression

p1 := y /. {First[Solve[x^2 + y^2 + x == 1, y, Reals]]}

{ConditionalExpression[-Sqrt[1 - x - x^2], 
   1/2 (-1 - Sqrt[5]) < x < 1/2 (-1 + Sqrt[5])]}

I want to get the -Sqrt[1 - x - x^2] out of the conditional expression and assign it to a variable. I don't care about the conditions, I'm aware of them and need the expression for use out of the ConditionalExpression. How do I do that?

I tried list commands combinations (Flatten, First, etc.) but they don't work with this. Am I just supposed to copy-paste?

Answer

You can use Normal, ConditionalExpression is not explicitly mentioned there but documentation says it deals with special forms.

p1 = y /. {First[Solve[x^2 + y^2 + x == 1, y, Reals]]} // First

 ConditionalExpression[-Sqrt[1 - x - x^2], 1/2 (-1 - Sqrt[5]) < x < 1/2 (-1 + Sqrt[5])]

Normal @ p1

-Sqrt[1 - x - x^2]

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