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So after much calculation F1 + F2 + F3 =0 F3 = -F1 - F2 F3 = -[-45i + 31j]-[120i - 44j] = 45i-31j-120i+44j = -75i + 13j


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up vote 0 down vote accepted

An object remains at rest if sum of all the forces applied on it is $0$. So, i think whatever you have done is correct (including computations).

Here, $x=-75$

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