Solve C_{1}=1/0.1[0.1*(0.1)^2/2*8.85*10^-12-10]

$$C _ { 1 } = \frac { 1 } { 0.1 } [ \frac { 0.1 \times ( 0.1 ) ^ { 2 } } { 2 \times 8.85 \times 10 ^ { - 12 } } - 10 ]$$

Solve for C_1

$$C_{1} = \frac{99999982300}{177} = 564971651\frac{73}{177} \approx 564971651.412429379$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$C_{1}=\frac{1}{0.1}\left(\frac{0.1^{3}}{2\times 8.85\times 10^{-12}}-10\right)$$

Expand \frac{1}{0.1} by multiplying both numerator and the denominator by 10. Anything divided by one gives itself.

$$C_{1}=10\left(\frac{0.1^{3}}{2\times 8.85\times 10^{-12}}-10\right)$$

Calculate 0.1 to the power of 3 and get 0.001.

$$C_{1}=10\left(\frac{0.001}{2\times 8.85\times 10^{-12}}-10\right)$$

Multiply 2 and 8.85 to get 17.7.

$$C_{1}=10\left(\frac{0.001}{17.7\times 10^{-12}}-10\right)$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$C_{1}=10\left(\frac{0.001}{17.7\times \frac{1}{1000000000000}}-10\right)$$

Multiply 17.7 and \frac{1}{1000000000000} to get \frac{177}{10000000000000}.

$$C_{1}=10\left(\frac{0.001}{\frac{177}{10000000000000}}-10\right)$$

Divide 0.001 by \frac{177}{10000000000000} by multiplying 0.001 by the reciprocal of \frac{177}{10000000000000}.

$$C_{1}=10\left(0.001\times \frac{10000000000000}{177}-10\right)$$

Multiply 0.001 and \frac{10000000000000}{177} to get \frac{10000000000}{177}.

$$C_{1}=10\left(\frac{10000000000}{177}-10\right)$$

Subtract 10 from \frac{10000000000}{177} to get \frac{9999998230}{177}.

$$C_{1}=10\times \frac{9999998230}{177}$$

Multiply 10 and \frac{9999998230}{177} to get \frac{99999982300}{177}.

$$C_{1}=\frac{99999982300}{177}$$

Assign C_1

$$C_{1}≔\frac{99999982300}{177}$$