Question why is there a negative sign

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The discussion revolves around the motion of a particle described by the equation x = 2 + 3t - 4t^2. The confusion arises regarding the use of a negative sign in the equation -x = -2 - 3t + 4t^2 when determining the particle's velocity upon returning to its initial position. The negative sign is used to express the condition that the particle's position x must equal its initial position of 2 meters, leading to the equation being set to zero. This reflects the mathematical approach to find when the particle returns to its starting point after changing direction. Understanding this step clarifies the reasoning behind the negative sign in the context of solving for the particle's velocity.
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A particle moves along the c axis. its position is given by the equation x = 2+3t-4t^2, with x in meters and t in seconds. Determine (a) its position when it changes direction and )b) its velocity when it returns to the position it had at t = 0.


i understand how to get (a) but for (b) I am confused why in the solution they put -x = -2-3t+4t^2 why is the negative there, i understand there is a change in direction at 0, I am confused why the negative sign is there can you give me a clear and understanding reasoning. thank you.
 
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I have no clue. They just randomly decided to flip the signs on everything, it looks like =/
 

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