Galaxy clusters are huge cosmic systems made of hundreds to thousands of galaxies, hot gas, and dark matter. NASA's Chandra X-ray Observatory has found gas in these clusters heated up to 100 million degrees. This hot gas, combined with energy from supermassive black holes at cluster centers, produces bubbles, waves, and other odd shapes. To understand these shapes better, astronomers developed a new method called X-arithmetic. This technique analyzes X-ray data more deeply by dividing it into lower- and higher-energy bands. It uses colors like pink for sound waves, yellow for black-hole bubbles, and blue for cooling gas to create clearer maps of the clusters. Scientists tested X-arithmetic on 15 galaxy clusters, including well-known ones like the Perseus and Virgo clusters. This method helps reveal how black holes release energy and shape their surroundings. These outbursts prevent gas from cooling too fast and control star formation. X-arithmetic offers a fresh look at the biggest cosmic giants and their hidden energy flows, bringing researchers closer to solving mysteries about galaxy clusters and their black holes.