When it comes to expressing an idea with strength, the word "well-supported" is an excellent choice. However, at times, using the same term can be monotonous and could lead to redundancy. Therefore, it's useful to have several synonyms at your disposal to keep writing fresh and diverse. Here are a few possibilities: backed, bolstered, buttressed, fortified, reinforced, substantiated, undergirded, validated, validated, verified and sustained. Each of these words conveys the same concept of an argument or idea being supported, but with a subtle nuance that could make all the difference depending on the context.