find all real solutions?

Question

x^2+x+√(x^2 +x)-2=0
I have no clue any help please

Answer 1

Hint: Try the substitution u = √x²+x
as this equation is quadratic in x²+x.
Then u²+u-2 = 0.
and u must be positive.
So (u+2)(u-1) = 0.
and u = 1.
So √x²+x = 1
x²+x-1 = 0
x = ½(-1 + √5)
and x = ½(-1-√5)
If x = ½(-1 + √5)
x² = ½(3- √5)
and x²+x = 1
so ½(-1 + √5) is a solution.
Similarly, if
x = ½(-1 - √5)
x² = ½(3 + √5)
and x²+x = 1.
So all real solutions are given by
x = ½(-1 + √5)
and
x = ½(-1 - √5).