Solve sigma_x^2=(-2-0)^2*4/9+(0*0)^2x

$$\sigma _ { x } ^ { 2 } = ( - 2 - 0 ) ^ { 2 } \times \frac { 4 } { 9 } + ( 0 \times 0 ) ^ { 2 } x$$

Solve for σ_x

$$\sigma _{x}=\frac{4}{3}$$

$$\sigma _{x}=-\frac{4}{3}$$

Steps by Finding Square Root

Subtract 0 from -2 to get -2.

$$\sigma _{x}^{2}=\left(-2\right)^{2}\times \frac{4}{9}+\left(0\times 0\right)^{2}x$$

Calculate -2 to the power of 2 and get 4.

$$\sigma _{x}^{2}=4\times \frac{4}{9}+\left(0\times 0\right)^{2}x$$

Multiply 4 and \frac{4}{9} to get \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(0\times 0\right)^{2}x$$

Multiply 0 and 0 to get 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}x$$

Calculate 0 to the power of 2 and get 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0x$$

Anything times zero gives zero.

$$\sigma _{x}^{2}=\frac{16}{9}+0$$

Add \frac{16}{9} and 0 to get \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}$$

Take the square root of both sides of the equation.

$$\sigma _{x}=\frac{4}{3} \sigma _{x}=-\frac{4}{3}$$

Steps Using the Quadratic Formula

Subtract 0 from -2 to get -2.

$$\sigma _{x}^{2}=\left(-2\right)^{2}\times \frac{4}{9}+\left(0\times 0\right)^{2}x$$

Calculate -2 to the power of 2 and get 4.

$$\sigma _{x}^{2}=4\times \frac{4}{9}+\left(0\times 0\right)^{2}x$$

Multiply 4 and \frac{4}{9} to get \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(0\times 0\right)^{2}x$$

Multiply 0 and 0 to get 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}x$$

Calculate 0 to the power of 2 and get 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0x$$

Anything times zero gives zero.

$$\sigma _{x}^{2}=\frac{16}{9}+0$$

Add \frac{16}{9} and 0 to get \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}$$

Subtract \frac{16}{9} from both sides.

$$\sigma _{x}^{2}-\frac{16}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{16}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\sigma _{x}=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{9}\right)}}{2}$$

Square 0.

$$\sigma _{x}=\frac{0±\sqrt{-4\left(-\frac{16}{9}\right)}}{2}$$

Multiply -4 times -\frac{16}{9}.

$$\sigma _{x}=\frac{0±\sqrt{\frac{64}{9}}}{2}$$

Take the square root of \frac{64}{9}.

$$\sigma _{x}=\frac{0±\frac{8}{3}}{2}$$

Now solve the equation \sigma _{x}=\frac{0±\frac{8}{3}}{2} when ± is plus.

$$\sigma _{x}=\frac{4}{3}$$

Now solve the equation \sigma _{x}=\frac{0±\frac{8}{3}}{2} when ± is minus.

$$\sigma _{x}=-\frac{4}{3}$$

The equation is now solved.

$$\sigma _{x}=\frac{4}{3} \sigma _{x}=-\frac{4}{3}$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$\sigma _{x}=\frac{4}{3}\text{ or }\sigma _{x}=-\frac{4}{3}$$

Solve for x

$$x\in \mathrm{R}$$

$$|\sigma _{x}|=\frac{4}{3}$$