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Why does borax help soften water?

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A labeled diagram of the periodic table entry for boron shows its atomic number 5, symbol B, electron configuration, atomic weight range, and classification as a solid, weakly acidic, other nonmetal with a rhombohedral crystal structure at room temperature. — boron Properties of boron.

Borax (sodium tetraborate decahydrate) acts as a water softener primarily due to two chemical properties:

Formation of Insoluble Precipitates: Borax reacts with the calcium and magnesium ions present in hard water to form insoluble borate compounds. By converting these dissolved minerals into an insoluble form, borax effectively removes them from the water, preventing them from interfering with soaps or forming scale in pipes and boilers.123
Alkaline Nature: Aqueous solutions of borax are basic (alkaline). This alkalinity assists in the softening process, often when used in conjunction with other agents like sodium carbonate (washing soda), which helps precipitate calcium as carbonate and magnesium as hydroxide.123

By removing these hardness-causing ions, borax prevents the formation of an insoluble gelatinous curd that otherwise occurs when soap reacts with hard water, thereby improving the effectiveness of cleaning agents.12