Question 1171982
The reason is when you take a square root of both sides of an equation, you now need the +/- on one side or else information is lost.<br>

Example
{{{ (x - 2)^2 = 25 }}}
{{{ sqrt((x - 2)^2) }}} = +/- {{{ sqrt(25) }}} (*)
{{{ x - 2 }}} = +/- {{{ 5 }}} 
{{{ x = 7 }}} or {{{ x = -3 }}}

If we only kept the positive root of both sides at (*), one answer would have been lost.
 
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In your specific problem, raising to the -3/2  is a raise tox the -3 followed by  the square root operation (or square root followed by raise to the -3), so that's where the square root is creeping in.

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Follow up: oh, I see what you mean.  I do not think the +/- needs to be added at that particular step, as you technically have not taken the sqrt(LHS) yet.  Once you write x by itself, then +/- is needed on RHS.   Remember though, it is the sqrt (multiple of 1/2 in the exponent) that is causing this need, not the fact that the exponent is negative.