Question

|x^2+x|=x^2+x.Solve for x.
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Answer 1

Answer:

Step-by-step explanation:

if x € (- infinity, - 1 ]U[0 , infinity) , then

x^2 + x >= 0 and the equation

|x^2 + x| is solvable for all x in the given interval.

if x € (- 1 , 0), then x^2 + x < 0 and then |x^2 + x| = - x^2 - x, that is

-x^2 - x = x^2 + x, that is, x^2 + x = 0, that is, x(x + 1) = 0, that is,

x= 0 or x = - 1. thus no solutions in this case.

Finally the solution set is

(- infinity, - 1 ]U[0 , infinity) .