Solve S=1/6[2(195-195)^2+2(194-195)^2+2(196-195)^2]=

$$S = \frac { 1 } { 6 } [ 2 ( 195 - 195 ) ^ { 2 } + 2 ( 194 - 195 ) ^ { 2 } + 2 ( 196 - 195 ) ^ { 2 } ] =$$

Solve for S

$$S=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Subtract 195 from 195 to get 0.

$$S=\frac{1}{6}\left(2\times 0^{2}+2\left(194-195\right)^{2}+2\left(196-195\right)^{2}\right)$$

Calculate 0 to the power of 2 and get 0.

$$S=\frac{1}{6}\left(2\times 0+2\left(194-195\right)^{2}+2\left(196-195\right)^{2}\right)$$

Multiply 2 and 0 to get 0.

$$S=\frac{1}{6}\left(0+2\left(194-195\right)^{2}+2\left(196-195\right)^{2}\right)$$

Subtract 195 from 194 to get -1.

$$S=\frac{1}{6}\left(0+2\left(-1\right)^{2}+2\left(196-195\right)^{2}\right)$$

Calculate -1 to the power of 2 and get 1.

$$S=\frac{1}{6}\left(0+2\times 1+2\left(196-195\right)^{2}\right)$$

Multiply 2 and 1 to get 2.

$$S=\frac{1}{6}\left(0+2+2\left(196-195\right)^{2}\right)$$

Add 0 and 2 to get 2.

$$S=\frac{1}{6}\left(2+2\left(196-195\right)^{2}\right)$$

Subtract 195 from 196 to get 1.

$$S=\frac{1}{6}\left(2+2\times 1^{2}\right)$$

Calculate 1 to the power of 2 and get 1.

$$S=\frac{1}{6}\left(2+2\times 1\right)$$

Multiply 2 and 1 to get 2.

$$S=\frac{1}{6}\left(2+2\right)$$

Add 2 and 2 to get 4.

$$S=\frac{1}{6}\times 4$$

Multiply \frac{1}{6} and 4 to get \frac{2}{3}.

$$S=\frac{2}{3}$$

Assign S

$$S≔\frac{2}{3}$$