The phrase "resolved to" means to make a decision or firm commitment to do something. Some synonyms for this phrase include determined, committed, dedicated, steadfast, resolute, and unwavering. Each of these words implies a strong sense of purpose and a willingness to see something through to the end. Other synonyms for "resolved to" include set on, intent on, and bent on, which convey an unwavering determination to achieve a specific goal. These synonyms can help to add variety and depth to one's writing, while also conveying a sense of determination and resolve.