Solve C_{3}=-1/0.1(10-0.1*0.1^2/2*8.85*10^-12)

$$C _ { 3 } = \frac { - 1 } { 0.1 } ( 10 - \frac { 0.1 \times 0.1 ^ { 2 } } { 2 \times 8.85 \times 10 ^ { - 12 } } )$$

Solve for C_3

$$C_{3} = \frac{99999982300}{177} = 564971651\frac{73}{177} \approx 564971651.412429379$$

Steps for Solving Linear Equation

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

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

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

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

Calculate 0.1 to the power of 3 and get 0.001.

$$C_{3}=-10\left(10-\frac{0.001}{2\times 8.85\times 10^{-12}}\right)$$

Multiply 2 and 8.85 to get 17.7.

$$C_{3}=-10\left(10-\frac{0.001}{17.7\times 10^{-12}}\right)$$

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

$$C_{3}=-10\left(10-\frac{0.001}{17.7\times \frac{1}{1000000000000}}\right)$$

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

$$C_{3}=-10\left(10-\frac{0.001}{\frac{177}{10000000000000}}\right)$$

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

$$C_{3}=-10\left(10-0.001\times \frac{10000000000000}{177}\right)$$

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

$$C_{3}=-10\left(10-\frac{10000000000}{177}\right)$$

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

$$C_{3}=-10\left(-\frac{9999998230}{177}\right)$$

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

$$C_{3}=\frac{99999982300}{177}$$

Assign C_3

$$C_{3}≔\frac{99999982300}{177}$$