How do you solve #|x^2+2x|=0#?

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Answer 1 · 2016-06-17T19:11:06

Simply removing the absolute value.

The absolute value can be solved considering two equations, one with the plus and one with the minus.

#|x^2+2x|=0#

#+(x^2+2x)=0#

#-(x^2+2x)=0#

In this case both equations are identical because you can multiply for #-1# left and right the equations transforming one in the other.

Then the solution is

#x^2+2x=0#

#x(x+2)=0# that has two solutions, one that is #x=0# and the other #x=-2#.