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Homework Statement:
 A spring is positioned vertical with the bottom end connected to ground. An object falls directly above the spring and when it almost hit the spring, it has speed of 3 m/s. Given that the mass of the object is 5 kg and the spring constant is 200 N/m, find the maximum compression of the spring
Relevant Equations:

Conservation of energy
KE = 1/2 m v^2
PE = mgh
Elastic potential energy = 1/2 k x^2
1/2 m v^{2} + mgh = 1/2 k x^{2}
1/2 (5) (9) + (5) (9.81) x = 1/2 (200) x^{2}
100 x^{2}  49.05 x  22.5 = 0
x = 0.779 m or x =  0.289 m
Answer key says the answer is 0.289 m but in my opinion the answer should be 0.799 m because I take h = 0 at the position where the spring has maximum compression so at the point where the object almost hit the spring the value of h should be positive, hence the value of x also should be positive.
Where is my mistake?
Thanks
1/2 (5) (9) + (5) (9.81) x = 1/2 (200) x^{2}
100 x^{2}  49.05 x  22.5 = 0
x = 0.779 m or x =  0.289 m
Answer key says the answer is 0.289 m but in my opinion the answer should be 0.799 m because I take h = 0 at the position where the spring has maximum compression so at the point where the object almost hit the spring the value of h should be positive, hence the value of x also should be positive.
Where is my mistake?
Thanks