check you quadratic equation for (1) again.....
you have x-x^2=2
then it should follow:
x^2-x+2=0 (you can use the quadratice equation formula)
you get x=2 or x=-1 (which you do, I am just making sure people understand what you did)
now just do what you would with (2) and you get the same factors right...
go ahead try plugging in (-1) for x in (2), it will not add upto 2!
only (2) works for x.....
you were almost there, but you have plug in the numbers to verify...
Regan used to say, "trust but verify"
I would say E but i took me around 3mn
for each abs value you have to imagine it can be negative or positive before executing the abolute value. For example :
|x-|x^2||=2 ; x-x^2=2; x^2-x-2=0 ; (x-2)(x+1) so 2 answers : 2 and -1
x-|x^2|=2 ; no need to check this, first go to statement (2) to see if you find different numbers than in (1)
X^2-x=2 ; x^2-x-2=0 ; (x-2)(x+1), same answer than in statement 1
even if there are other possibilities, you've already found 2 different possible answers which are 2 and -1 in both statements so you can not choose any value for sure. E. no need to calculate everything.