Vector Problem(Physics)

You are given a vector in the xy plane that has a magnitude of 83.0 units and a y component of -63.0 units.

Assuming the x component is known to be positive, specify the vector V which, if you add it to the original one, would give a resultant vector that is 69.0 units long and points entirely in the -x direction.

To organize your given information make a table with 3 rows and 3 columns
Label the columns "vector 1", "vector 2", & "Resultant"
Label the rows "x component", "y component", & "magnitude"
Then fill in your givens:
****The magnitude of vector 1 is 83.0
****The y component of vector 1 is -63.0
****The x component of vector 1 has a + sign
****The Resultant vector has a magnitude of 69.0
****The y component of the Resultant vector is 0 (implied)
You know nothing about vector 2 except that it is the vector difference between the Resultant vector and vector 1.
You can solve the problem using nothing but arithmetic.
First, note that if the Resultant vector lies entirely in the -x direction so its x component is -69.0
Next, calculate x component of vector 1 = sq. root ( 83^2 - -63^2) = 54
Then, the x component of vector 2 = -69 - 54 = -123
And, the y component of vector 2 = 0 - -63 = 63
Finally, the magnitude of vector 2 = sq. root ( -123^2 + 63^2 ) = 138.2