M3 Newton's law of gravitation question

In the following questionthe partucle is moving towards the centre of the earth which means the same direction as the acceleration. I took it that this means that F = (GmM)/(x^2) instead of F = (-GmM)/(x^2) is my assumption wrong? The correct answer as given in the book only comes if F = (-GmM)/(x^2). I attached my working.

I had this exact problem about a month ago. After asking @Zacken , I think he said something on the lines of the reason why the force/acceleration is negative is because the displacement x from the earth is decreasing as the particle is in motion. I still struggle to get my head around this but I guess you could always use common sense, e.g if the speed at the surface isn't greater than the original speed then you know you have ****ed up somewhere