We have produced hard x-ray free-electron laser (FEL) radiation with unprecedented large bandwidth tunable up to 2%. The experiments have been carried out at SwissFEL, the x-ray FEL facility at the Paul Scherrer Institute in Switzerland. The bandwidth is enhanced by maximizing the energy chirp of the electron beam, which is accomplished by optimizing the compression setup. We demonstrate continuous tunability of the bandwidth with a simple method only requiring a quadrupole magnet. The generation of such broadband FEL pulses will improve the efficiency of many techniques such as x-ray crystallography and spectroscopy, opening the door to significant progress in photon science. It has already been demonstrated that the broadband pulses of SwissFEL are beneficial to enhance the performance of crystallography, and further SwissFEL users plan to exploit this large bandwidth radiation to improve the efficiency of their measurement techniques.