What is the answer to 0.001=(1/(1+0.5x))^2 ?

The answer to 0.001=(1/(1+0.5x))^2 is x=2(10sqrt(10)-1),x=-2(10sqrt(10)+1)

Solve for x: 0.001=(1/(1+0.5x))^2

The solution is x=2(10sqrt(10)-1),x=-2(10sqrt(10)+1)

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0.001 = (\frac{1}{1 + 0.5 x})^{2}

x = 2 (1010 - 1), x = - 2 (1010 + 1)

Decimal Notation

x = 61.24555 \dots, x = - 65.24555 \dots

Solution steps

0.001 = (\frac{1}{1 + 0.5 x})^{2}

Simplify

(\frac{1}{1 + 0.5 x})^{2} : \frac{1}{( 1 + 0.5 x ) ^{2}}

0.001 = \frac{1}{( 1 + 0.5 x ) ^{2}}

Multiply both sides by

(1 + 0.5 x)^{2}

0.001 (1 + 0.5 x)^{2} = 1

Solve

0.001 (1 + 0.5 x)^{2} = 1 : x = 2 (1010 - 1), x = - 2 (1010 + 1)

x = 2 (1010 - 1), x = - 2 (1010 + 1)

Verify Solutions

Find undefined (singularity) points:

x = - 2

Combine undefined points with solutions:

x = 2 (1010 - 1), x = - 2 (1010 + 1)

\frac{4}{5} = \frac{6}{b} - 1

25 = \frac{15 - 8 x}{8 x} \cdot 100

x - \frac{1}{x} = 8

\frac{1}{x} = \frac{6}{5 x}

\frac{3}{x} - \frac{5}{x - 1} = 4

What is the answer to 0.001=(1/(1+0.5x))^2 ?
The answer to 0.001=(1/(1+0.5x))^2 is x=2(10sqrt(10)-1),x=-2(10sqrt(10)+1)
Solve for x: 0.001=(1/(1+0.5x))^2
The solution is x=2(10sqrt(10)-1),x=-2(10sqrt(10)+1)