Solve {l}{-4.9*2+s_2^2=1/6[(99-100)^{2}+(100-100)^2+}{(102-100)^2+(99-100)^2+(100-100)^2+}

$$\left. \begin{array}{l}{ - 4.9 \times 2 + s _ { 2 } ^ { 2 } = \frac { 1 } { 6 } [ ( 99 - 100 ) ^ { 2 } + ( 100 - 100 ) ^ { 2 } + }\\{ ( 102 - 100 ) ^ { 2 } + ( 99 - 100 ) ^ { 2 } + ( 100 - 100 ) ^ { 2 } + }\end{array} \right.$$

Solve for s_2

$$s_{2} = \frac{\sqrt{8970}}{30} \approx 3.157002798$$

$$s_{2} = -\frac{\sqrt{8970}}{30} \approx -3.157002798$$

Steps by Finding Square Root

Multiply -4.9 and 2 to get -9.8.

$$-9.8+s_{2}^{2}=\frac{1}{6}$$

Add 9.8 to both sides.

$$s_{2}^{2}=\frac{1}{6}+9.8$$

Add \frac{1}{6} and 9.8 to get \frac{299}{30}.

$$s_{2}^{2}=\frac{299}{30}$$

Take the square root of both sides of the equation.

$$s_{2}=\frac{\sqrt{8970}}{30} s_{2}=-\frac{\sqrt{8970}}{30}$$

Steps Using the Quadratic Formula

Multiply -4.9 and 2 to get -9.8.

$$-9.8+s_{2}^{2}=\frac{1}{6}$$

Subtract \frac{1}{6} from both sides.

$$-9.8+s_{2}^{2}-\frac{1}{6}=0$$

Subtract \frac{1}{6} from -9.8 to get -\frac{299}{30}.

$$-\frac{299}{30}+s_{2}^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$s_{2}^{2}-\frac{299}{30}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{299}{30} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s_{2}=\frac{0±\sqrt{0^{2}-4\left(-\frac{299}{30}\right)}}{2}$$

Square 0.

$$s_{2}=\frac{0±\sqrt{-4\left(-\frac{299}{30}\right)}}{2}$$

Multiply -4 times -\frac{299}{30}.

$$s_{2}=\frac{0±\sqrt{\frac{598}{15}}}{2}$$

Take the square root of \frac{598}{15}.

$$s_{2}=\frac{0±\frac{\sqrt{8970}}{15}}{2}$$

Now solve the equation s_{2}=\frac{0±\frac{\sqrt{8970}}{15}}{2} when ± is plus.

$$s_{2}=\frac{\sqrt{8970}}{30}$$

Now solve the equation s_{2}=\frac{0±\frac{\sqrt{8970}}{15}}{2} when ± is minus.

$$s_{2}=-\frac{\sqrt{8970}}{30}$$

The equation is now solved.

$$s_{2}=\frac{\sqrt{8970}}{30} s_{2}=-\frac{\sqrt{8970}}{30}$$