Directional Sleeve Weight For Target Alpha

A portfolio mixes a market-neutral arbitrage sleeve with realized return 4% and beta 0.2, and a directional sleeve with realized return 14% and beta 1.4. Let w be the weight in the directional sleeve and 1-w in the arbitrage sleeve. If the risk-free rate is 2% and the market returned 8%, what value of w makes the combined portfolio alpha exactly 2.2%?