Bring radical

Summary

The Bring radical of a real number $a$ is the unique real root of $x^5 + x + a$. It plays for quintic equations the role that $n$-th roots play for the equations $x^n = a$. Using only radicals, every quintic equation can be reduced to the Bring–Jerrard form $x^5 + px + q = 0$. With the Bring radical extended to complex arguments, the roots of every quintic can then be written with radicals and Bring radicals.