What is the answer to x^{-2}+2x^{-1}-8=0 ?

The answer to x^{-2}+2x^{-1}-8=0 is x=-1/4 ,x= 1/2

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x^{-2}+2x^{-1}-8=0

x^{- 2} + 2 x^{- 1} - 8 = 0

x = - \frac{1}{4}, x = \frac{1}{2}

Solution steps

x^{- 2} + 2 x^{- 1} - 8 = 0

Refine

\frac{1}{x ^{2}} + \frac{2}{x} - 8 = 0

Multiply by LCM

1 + 2 x - 8 x^{2} = 0

Solve

1 + 2 x - 8 x^{2} = 0 : x = - \frac{1}{4}, x = \frac{1}{2}

x = - \frac{1}{4}, x = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{1}{4}, x = \frac{1}{2}

2 - \frac{1}{7 x} = \frac{10}{7}

\frac{x}{2 x + 7} = \frac{x - 5}{x - 1}

\frac{x - 4}{3 x + 2} = \frac{3}{7}

\frac{1}{x} = \frac{x + 3}{2 x ^{2}}

\frac{15}{x - 1} = \frac{19}{x + 4}

What is the answer to x^{-2}+2x^{-1}-8=0 ?
The answer to x^{-2}+2x^{-1}-8=0 is x=-1/4 ,x= 1/2
Solve for x: x^{-2}+2x^{-1}-8=0
The solution is x=-1/4 ,x= 1/2