What is the answer to 5.916x=1-(1/(1+x))^{10} ?

The answer to 5.916x=1-(1/(1+x))^{10} is x=0,x\approx 0.10891…,x\approx-1.78297…

Solve for x: 5.916x=1-(1/(1+x))^{10}

The solution is x=0,x\approx 0.10891…,x\approx-1.78297…

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5.916 x = 1 - (\frac{1}{1 + x})^{10}

x = 0, x \approx 0.10891 \dots, x \approx - 1.78297 \dots

Solution steps

5.916 x = 1 - (\frac{1}{1 + x})^{10}

Multiply both sides by

1000

5916 x = 1000 - \frac{1000}{( 1 + x ) ^{10}}

Multiply both sides by

(1 + x)^{10}

5916 x (1 + x)^{10} = 1000 (1 + x)^{10} - 1000

Solve

5916 x (1 + x)^{10} = 1000 (1 + x)^{10} - 1000 : x = 0, x \approx 0.10891 \dots, x \approx - 1.78297 \dots

x = 0, x \approx 0.10891 \dots, x \approx - 1.78297 \dots

Verify Solutions

Find undefined (singularity) points:

x = - 1

Combine undefined points with solutions:

x = 0, x \approx 0.10891 \dots, x \approx - 1.78297 \dots

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

2 x - \frac{12}{2 - x} = 7 + \frac{11 x + 11}{9}

\frac{7}{x + 4} - \frac{1}{x} = \frac{8}{15}

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

\frac{6}{m} + 2 = \frac{m + 3}{m - 1}

What is the answer to 5.916x=1-(1/(1+x))^{10} ?
The answer to 5.916x=1-(1/(1+x))^{10} is x=0,x\approx 0.10891…,x\approx-1.78297…
Solve for x: 5.916x=1-(1/(1+x))^{10}
The solution is x=0,x\approx 0.10891…,x\approx-1.78297…