Solve s_1^2=frac{(4-9,6)^{2}+(8-9,6)^2+(9-9,6)^2+(11-9,6)^2+(16-9,6)^2}{5}

$$s _ { 1 } ^ { 2 } = \frac { ( 4 - 9,6 ) ^ { 2 } + ( 8 - 9,6 ) ^ { 2 } + ( 9 - 9,6 ) ^ { 2 } + ( 11 - 9,6 ) ^ { 2 } + ( 16 - 9,6 ) ^ { 2 } } { 5 }$$

Solve for s_1

$$s_{1} = \frac{\sqrt{386}}{5} \approx 3.929376541$$

$$s_{1} = -\frac{\sqrt{386}}{5} \approx -3.929376541$$

Steps by Finding Square Root

Multiply both sides of the equation by 5.

$$5s_{1}^{2}=\left(4-9,6\right)^{2}+\left(8-9,6\right)^{2}+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 4 to get -5,6.

$$5s_{1}^{2}=\left(-5,6\right)^{2}+\left(8-9,6\right)^{2}+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Calculate -5,6 to the power of 2 and get 31,36.

$$5s_{1}^{2}=31,36+\left(8-9,6\right)^{2}+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 8 to get -1,6.

$$5s_{1}^{2}=31,36+\left(-1,6\right)^{2}+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Calculate -1,6 to the power of 2 and get 2,56.

$$5s_{1}^{2}=31,36+2,56+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Add 31,36 and 2,56 to get 33,92.

$$5s_{1}^{2}=33,92+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 9 to get -0,6.

$$5s_{1}^{2}=33,92+\left(-0,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Calculate -0,6 to the power of 2 and get 0,36.

$$5s_{1}^{2}=33,92+0,36+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Add 33,92 and 0,36 to get 34,28.

$$5s_{1}^{2}=34,28+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 11 to get 1,4.

$$5s_{1}^{2}=34,28+1,4^{2}+\left(16-9,6\right)^{2}$$

Calculate 1,4 to the power of 2 and get 1,96.

$$5s_{1}^{2}=34,28+1,96+\left(16-9,6\right)^{2}$$

Add 34,28 and 1,96 to get 36,24.

$$5s_{1}^{2}=36,24+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 16 to get 6,4.

$$5s_{1}^{2}=36,24+6,4^{2}$$

Calculate 6,4 to the power of 2 and get 40,96.

$$5s_{1}^{2}=36,24+40,96$$

Add 36,24 and 40,96 to get 77,2.

$$5s_{1}^{2}=77,2$$

Divide both sides by 5.

$$s_{1}^{2}=\frac{77,2}{5}$$

Expand \frac{77,2}{5} by multiplying both numerator and the denominator by 10.

$$s_{1}^{2}=\frac{772}{50}$$

Reduce the fraction \frac{772}{50} to lowest terms by extracting and canceling out 2.

$$s_{1}^{2}=\frac{386}{25}$$

Take the square root of both sides of the equation.

$$s_{1}=\frac{\sqrt{386}}{5} s_{1}=-\frac{\sqrt{386}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 5.

$$5s_{1}^{2}=\left(4-9,6\right)^{2}+\left(8-9,6\right)^{2}+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 4 to get -5,6.

$$5s_{1}^{2}=\left(-5,6\right)^{2}+\left(8-9,6\right)^{2}+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Calculate -5,6 to the power of 2 and get 31,36.

$$5s_{1}^{2}=31,36+\left(8-9,6\right)^{2}+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 8 to get -1,6.

$$5s_{1}^{2}=31,36+\left(-1,6\right)^{2}+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Calculate -1,6 to the power of 2 and get 2,56.

$$5s_{1}^{2}=31,36+2,56+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Add 31,36 and 2,56 to get 33,92.

$$5s_{1}^{2}=33,92+\left(9-9,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 9 to get -0,6.

$$5s_{1}^{2}=33,92+\left(-0,6\right)^{2}+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Calculate -0,6 to the power of 2 and get 0,36.

$$5s_{1}^{2}=33,92+0,36+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Add 33,92 and 0,36 to get 34,28.

$$5s_{1}^{2}=34,28+\left(11-9,6\right)^{2}+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 11 to get 1,4.

$$5s_{1}^{2}=34,28+1,4^{2}+\left(16-9,6\right)^{2}$$

Calculate 1,4 to the power of 2 and get 1,96.

$$5s_{1}^{2}=34,28+1,96+\left(16-9,6\right)^{2}$$

Add 34,28 and 1,96 to get 36,24.

$$5s_{1}^{2}=36,24+\left(16-9,6\right)^{2}$$

Subtract 9,6 from 16 to get 6,4.

$$5s_{1}^{2}=36,24+6,4^{2}$$

Calculate 6,4 to the power of 2 and get 40,96.

$$5s_{1}^{2}=36,24+40,96$$

Add 36,24 and 40,96 to get 77,2.

$$5s_{1}^{2}=77,2$$

Subtract 77,2 from both sides.

$$5s_{1}^{2}-77,2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -77,2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s_{1}=\frac{0±\sqrt{0^{2}-4\times 5\left(-77,2\right)}}{2\times 5}$$

Square 0.

$$s_{1}=\frac{0±\sqrt{-4\times 5\left(-77,2\right)}}{2\times 5}$$

Multiply -4 times 5.

$$s_{1}=\frac{0±\sqrt{-20\left(-77,2\right)}}{2\times 5}$$

Multiply -20 times -77,2.

$$s_{1}=\frac{0±\sqrt{1544}}{2\times 5}$$

Take the square root of 1544.

$$s_{1}=\frac{0±2\sqrt{386}}{2\times 5}$$

Multiply 2 times 5.

$$s_{1}=\frac{0±2\sqrt{386}}{10}$$

Now solve the equation s_{1}=\frac{0±2\sqrt{386}}{10} when ± is plus.

$$s_{1}=\frac{\sqrt{386}}{5}$$

Now solve the equation s_{1}=\frac{0±2\sqrt{386}}{10} when ± is minus.

$$s_{1}=-\frac{\sqrt{386}}{5}$$

The equation is now solved.

$$s_{1}=\frac{\sqrt{386}}{5} s_{1}=-\frac{\sqrt{386}}{5}$$