Reciprocal Quartic Equation

Solve the equation $x^{4} + x^{3} - 4 x^{2} + x + 1 = 0$ .

~6 minAnswer checked instantlypalindromic polynomialsubstitutionquartics

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.a, No. 35

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).