successfully
In a way that reaches the goal or desired result.
To do something successfully means to accomplish what you set out to do, achieving the result you wanted or needed. When you study for a spelling test and get all the words right, you've completed it successfully. When a baker successfully makes a soufflé (a tricky dessert that often falls flat), it rises perfectly and tastes delicious.
The word describes the outcome of effort and planning. A scientist who successfully launches a rocket has managed all the complex calculations, engineering, and timing required. A student who successfully builds friendships at a new school has navigated the challenge of meeting people and forming connections.
Success often requires persistence. Thomas Edison successfully invented the light bulb after hundreds of failed attempts. The Apollo 13 astronauts successfully returned to Earth despite a catastrophic oxygen tank explosion that could have killed them, thanks to creative problem-solving under pressure.
Notice that successfully doesn't always mean perfectly. A gymnast might successfully complete a routine even with a small wobble on the balance beam. What matters is achieving the main goal, whether that's finishing a difficult book, training your dog to sit on command, or persuading your parents that your science fair idea is worth pursuing.