Решите уравнение: 64x+x^-1=-16.

\[64x + x^{- 1} = - 16\ \ \ | \cdot x\]

\[64x^{2} + x^{0} = - 16x\]

\[64x^{2} + 16x + 1 = 0\]

\[(8x + 1)^{2} = 0\]

\[8x + 1 = 0\]

\[8x = - 1\]

\[x = - \frac{1}{8}.\]

\[Ответ:x = - \frac{1}{8}.\]