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

The answer to x^{-2}+2x+1=0 is x=-1,x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4

Solve for x: x^{-2}+2x+1=0

The solution is x=-1,x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4

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

x = - 1, x = \frac{1}{4} + i \frac{7}{4}, x = \frac{1}{4} - i \frac{7}{4}

Solution steps

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

Refine

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

Multiply both sides by

x^{2}

1 + 2 x^{3} + x^{2} = 0

Solve

1 + 2 x^{3} + x^{2} = 0 : x = - 1, x = \frac{1}{4} + i \frac{7}{4}, x = \frac{1}{4} - i \frac{7}{4}

x = - 1, x = \frac{1}{4} + i \frac{7}{4}, x = \frac{1}{4} - i \frac{7}{4}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - 1, x = \frac{1}{4} + i \frac{7}{4}, x = \frac{1}{4} - i \frac{7}{4}

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

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

\frac{x + 2}{x + 5} = \frac{2}{3}

a, r = \frac{ab}{a + b}

y, x = \frac{1}{y + 2}

What is the answer to x^{-2}+2x+1=0 ?
The answer to x^{-2}+2x+1=0 is x=-1,x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4
Solve for x: x^{-2}+2x+1=0
The solution is x=-1,x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4