Capacitor needed for phase angle change (RLC network)

[D.B0004]

Homework Statement

An inductive load is connected to a 120V (rms), 60Hz AC source. The load draws 5.0 kW at a power factor of 0.81 (lagging). You need to improve your power factor to 0.96 (lagging) by adding a capacitor.

What is the Capacitance needed (in uF)?

Homework Equations

P/|S| = cos(phi)
Q = V^2/X
S = sqrt(P^2 + Q^2)

The Attempt at a Solution

Please see photo with my solution attached. My professor says the answer is actually 398.17uF. I did this problem multiple times and never got that answer. I keep getting what I got in the photo attached (271uF).

 

[gneill]

It's hard to make out your work in that sideways photo. Can you explain your approach?