Determine the solution.

Question

x^2=|x|algebraically

I have no idea how to proceed with this. Can you please help?

Answer 1

x²=|x|
means
A. x²=x, or
B. x²=-x

The only solution for case B in the real domain (ℝ) is x=0.

Now let us look at case A.
x²=x
x²-x=0
x(x-1)=0
Can you complete the calculations?

Answer 2

Ok, so I got
x=0 x=1
x=0 x=-1
is that right?

Answer 3

Yes, your solutions are correct.
I have overlooked the root -1 for case B.
(-1)²+(-1)=0
Well done!

Answer 4

Thank you for your guidance! Have a great night.

Answer 5

Thank you, same to you too!