mathematica General::ivar ... is not a valid variable - replace

Question

I have the following problem in Mathematica:
values = {b -> 1, c -> 0};
Solutions := Solve[x^2 + b*x + c == 0, x]
x1 := x /. Solutions[[1]];
x2 := x /. Solutions[[2]];
"Solution 1"
x1
"Solution 2"
x2
"Choose ~preferred~ Solution, which is -1 when using values"
If[Module[{list = values}, ReplaceRepeated[x1 == -1, list]], x = x1, x = x2]
"~Preferred~ Solution"
x
When I evaluate it the first time,everything works:
Solution 1
1/2 (-b - Sqrt[b^2 - 4 c])
Solution 2
1/2 (-b + Sqrt[b^2 - 4 c])
Choose ~preferred~ Solution, which is -1 when using values
1/2 (-b - Sqrt[b^2 - 4 c])
But by evaluate it a second time several errors occurs:
Solution 1
General::ivar: 1/2 (-b-Sqrt[b^2-4 c]) is not a valid variable. >>
General::ivar: 1/2 (-b-Sqrt[b^2-4 c]) is not a valid variable. >>
ReplaceAll::reps: {1/2 b (-b-Sqrt[Plus[<<2>>]])+1/4 (-b-Power[<<2>>])^2+c==0} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
1/2 (-b - Sqrt[b^2 - 4 c]) /.
1/2 b (-b - Sqrt[b^2 - 4 c]) + 1/4 (-b - Sqrt[b^2 - 4 c])^2 + c == 0
"Solution 2"
...
It seems to me, that the ReplaceRepeated in the if condition work global although it is a Module environment. Can anybody help? How I solve this problem?

Answer 1

Evaluate your code the first time
In[1]:= values = {b -> 1, c -> 0};
Solutions := Solve[x^2 + b*x + c == 0, x]
x1 := x /. Solutions[[1]];
x2 := x /. Solutions[[2]];
"Solution 1"
x1
"Solution 2"
x2
"Choose ~preferred~ Solution, which is -1 when using values"
If[Module[{list = values}, ReplaceRepeated[x1 == -1, list]], x = x1, x = x2]
"~Preferred~ Solution"
x
Out[5]= "Solution 1"
Out[6]= 1/2 (-b - Sqrt[b^2 - 4 c])
Out[7]= "Solution 2"
Out[8]= 1/2 (-b + Sqrt[b^2 - 4 c])
Out[9]= "Choose ~preferred~ Solution, which is -1 when using values"
Out[10]= 1/2 (-b - Sqrt[b^2 - 4 c])
Out[11]= "~Preferred~ Solution"
Out[12]= 1/2 (-b - Sqrt[b^2 - 4 c])
All that is fine. What is the value of x now?
In[13]:= x
Out[13]= 1/2 (-b - Sqrt[b^2 - 4 c])
That is fine. Now begin to evaluate your code a second time.
In[14]:= values = {b -> 1, c -> 0};
Solutions := Solve[x^2 + b*x + c == 0, x]
Suppose you want to evaluate Solutions now. That is going to evaluate your quadratic in x, but you see x is no longer just a symbol with no value, it is going to use the value of x in Out[13] and Solutions is
In[15]:= Solutions
During evaluation of In[15]:= Solve::ivar: 1/2 (-b-Sqrt[b^2-4 c]) is not a valid variable. >>
Out[15]= Solve[1/2b(-b-Sqrt[b^2-4c])+1/4(-b-Sqrt[b^2-4c])^2+c==0, 1/2(-b-Sqrt[b^2-4c])]
And that is why it fails. You previously assigned x a value, you are using x and thus that value in your Solve. Perhaps you want to Clear your x before evaluating all this.