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We derive the Cardano formula of cubic equations by completing the cube, andprovide radical solutions to some algebraic equations of higher degree bycompleting powers. The main idea of completing powers arises from Harrison'scenter theory of higher degree forms. A very simple criterion for suchalgebraic equations is presented, and the computation amounts to solving linearequations and quadratic equations.

Solving cubic equations by completing the cube and higher degree equations by completing powers