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  "body": "\n## Summary\n\nThe Bring radical of a real number $a$ is the unique real root of $x^5 + x + a$.\nIt plays for quintic equations the role that $n$-th roots play for the equations $x^n = a$.\nUsing only radicals, every quintic equation can be reduced to the Bring–Jerrard form $x^5 + px + q = 0$.\nWith the Bring radical extended to complex arguments, the roots of every quintic can then be written with radicals and Bring radicals.\n\n## Explanations\n\n### L1 human\n\nThe [[Abel–Ruffini theorem|163A2WQQJX]] says that ordinary roots are not enough to solve all quintic equations.\nThe Bring radical is a new kind of root that fills this gap.\nJust as $\\sqrt[3]{a}$ is the real number whose cube is $a$, the Bring radical of $a$ is the real number $x$ with $x^5 + x = -a$.\nFor example, the Bring radical of $-2$ is $1$, since $1^5 + 1 - 2 = 0$.\n",
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