While Proof-of-Work (PoW) is the most widely used consensus mechanism for blockchain, it received harsh criticism due to its massive waste of energy for meaningless hash calculation. Some studies have introduced Proof-of-Stake to address this issue. However, such protocols widen the gap between rich and poor and in the worst case lead to an oligopoly, where the rich control the entire network. Other studies have attempted to translate the energy consumption of PoW into useful work, but they have many limitations, such as narrow application scope, serious security issues and impractical incentive model. In this paper, we introduce AxeChain, which can use the computing power of blockchain to solve practical problems raised by users without greatly compromising decentralization or security. AxeChain achieves this by coupling hard problem solving with PoW mining. We model the security of AxeChain and derive a balance curve between power utilization and system security. That is, under the reasonable assumption that the attack power does not exceed 1/3 of the total power, 1/2 of total power can be safely used to solve practical problems. We also design a novel incentive model based on the amount of work involved in problem solving, balancing the interests of both the users and miners. Moreover, our experimental results show that AxeChain provides strong security guarantees, no matter what kind of problem is submitted.