What is the answer to x^{-2}-x^{-1}-42=0 ?

The answer to x^{-2}-x^{-1}-42=0 is x=-1/6 ,x= 1/7

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x^{-2}-x^{-1}-42=0

x^{- 2} - x^{- 1} - 42 = 0

x = - \frac{1}{6}, x = \frac{1}{7}

Decimal Notation

x = - 0.16666 \dots, x = 0.14285 \dots

Solution steps

x^{- 2} - x^{- 1} - 42 = 0

Refine

\frac{1}{x ^{2}} - \frac{1}{x} - 42 = 0

Multiply by LCM

1 - x - 42 x^{2} = 0

Solve

1 - x - 42 x^{2} = 0 : x = - \frac{1}{6}, x = \frac{1}{7}

x = - \frac{1}{6}, x = \frac{1}{7}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{1}{6}, x = \frac{1}{7}

\frac{3 x}{8 + 4} = \frac{x - 2}{x}

\frac{x ^{2} - 5 x + 6}{x} = 3

\frac{12}{x + 5} = 4

\frac{4}{n + 5} = \frac{7}{8}

\frac{7.4}{x} = 1.43

What is the answer to x^{-2}-x^{-1}-42=0 ?
The answer to x^{-2}-x^{-1}-42=0 is x=-1/6 ,x= 1/7
Solve for x: x^{-2}-x^{-1}-42=0
The solution is x=-1/6 ,x= 1/7