What is the answer to x^{-2}-x^{-1}-6=0 ?

The answer to x^{-2}-x^{-1}-6=0 is x=-1/2 ,x= 1/3

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x^{-2}-x^{-1}-6=0

x^{- 2} - x^{- 1} - 6 = 0

x = - \frac{1}{2}, x = \frac{1}{3}

Decimal Notation

x = - 0.5, x = 0.33333 \dots

Solution steps

x^{- 2} - x^{- 1} - 6 = 0

Refine

\frac{1}{x ^{2}} - \frac{1}{x} - 6 = 0

Multiply by LCM

1 - x - 6 x^{2} = 0

Solve

1 - x - 6 x^{2} = 0 : x = - \frac{1}{2}, x = \frac{1}{3}

x = - \frac{1}{2}, x = \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{1}{2}, x = \frac{1}{3}

\frac{( 2 x ^{2} + 9 x - 5 )}{( x ^{4} + 1 )} = 0

437 = \frac{( x + 7 )}{2 \cdot 3 ( - 4 + x )}

\frac{1}{2 x [ \frac{3}{4} + x ]} = - \frac{7}{10}

\frac{( n - 8 ) !}{( n - 9 ) !} = 9

\frac{9}{x ^{4}} + \frac{8}{x ^{2}} = 1

What is the answer to x^{-2}-x^{-1}-6=0 ?
The answer to x^{-2}-x^{-1}-6=0 is x=-1/2 ,x= 1/3
Solve for x: x^{-2}-x^{-1}-6=0
The solution is x=-1/2 ,x= 1/3