Find all real solutions to each equation?

Question

x^2+x+ *sqrt*[x^2+x] - 2 = 0

Am I to just arrange the data like this?

x^2 + x - 2 = - *sqrt* [x^2 +x]

Answer 1

let u = sqrt(x^2 +x)

u^2 + u - 2 = 0
(u+2)(u-1) = 0

u = -2 and u = 1

sqrt(x^2 +x) = -2

Will not yield real solutions.

Also

sqrt(x^2+x) = 1
x^2 + x = 1
x^2 +x -1 = 0

quadratic equation:

x = 0.618 and x = -1.618

Answer 2

Now square both sides.
Collect like terms.
Solve.
Be sure to check answer as the squaring may introduce extraneous roots.

What is the purpose of the two * ?