Solving a Vector Problem in the xy Plane

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To solve the vector problem, the x component can be determined using the Pythagorean theorem, yielding two possibilities: x = 40.0 or x = -40.0. Given that the x component is positive, the vector is (40.0, -60.0). To achieve a resultant vector of 70.0 units pointing in the -x direction, a vector with components (-70.0, 0) must be added to the original vector. The equation linking the components x, y, and magnitude r is r = √(x² + y²). This discussion emphasizes the application of vector addition and the relationship between components and magnitude in the xy plane.
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Here is the problem I can't solve:

You are given a vector in the xy plane that has a magnitude of 80.0 units and a y component of -60.0 units.

(a) What are the two possibilities for its x component?

(b) Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 70.0 units long and points entirely in the -x direction. (looking for Magnitude + Direction)
 
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