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A new method of designing x-ray supermirrors with broad angular or energy response for use as coatings in x-ray optics is presented. The design is based on an analytical method with oversimplified analytical and semi-empirical formulae, and an extensive numerical method is used in the optimization design. A better initial multilayer is obtained with the former method and optimized with the latter method. In the optimization, a good design is achieved with much less computing time. In addition, the saturation effect due to the interfacial roughness in multilayer also emerges in the design of x-ray supermirrors with definite performances. The reflectivity of C/W x-ray supermirrors as a function of photon energy at the fixed grazing incident angle 0.5° is presented.