SOLUTION: Can somebody please help me! Find all real solutions to (a) x^2 + x + SQRT(x^2 + x) - 2 = 0 I have been working on this problems for a couple of days and I can't seem t

Question 61003This question is from textbook
: Can somebody please help me!
Find all real solutions to
(a) x^2 + x + SQRT(x^2 + x) - 2 = 0
I have been working on this problems for a couple of days and I can't seem to understand, or even know what to do. I know I need to use the substitution methods but the radical in the equation is confusing me.
This question is from textbook

Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Find all real solutions to
(a)
Use the substitution method.

Let
Factor
(P+2)(P-1)=0
P+2=0 and P-1=0
P=-2 and P=1
But we want to know what x is, so let
and
and
and
and
You have to use the quadratic equation to solve these:

when a=1, b=1, c=-4

You have to check these to see if they are valid or extraneous. I checked these by plugging them into my calculator and the were both extraneous.
when a=1, b=1, and c=-1

You have to check these to see if they are valid or extraneous. I checked these with my calculator and they were both valid.
If you have a TI-83 or 84, I can give you instructions on checking for extraneous solutions if you ask.
Happy Calculating!!!
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