If that is the correct base64 encoding of your user:password, then:
if (client.connect(server,80)) {
Serial.println("connected");
// Make a HTTP request:
client.println("GET /search?q=arduino HTTP/1.1");
client.println("Authorization: Basic QzF5WXIxXG15cW14FkJheWVyMTIz");
client.println("Host: www.google.com");
client.println("Connection: Close");
client.println();