Resolver sigma_x^2=(-2-0)^2*4/9+(0*0)^2*3/9+(1*9)^2*2/9

$$\sigma _ { x } ^ { 2 } = ( - 2 - 0 ) ^ { 2 } \times \frac { 4 } { 9 } + ( 0 \times 0 ) ^ { 2 } \times \frac { 3 } { 9 } + ( 1 \times 9 ) ^ { 2 } \times \frac { 2 } { 9 }$$

Resolver σ_x

$$\sigma _{x}=\frac{\sqrt{178}}{3}\approx 4.447221355$$

$$\sigma _{x}=-\frac{\sqrt{178}}{3}\approx -4.447221355$$

Pasos para obter a raíz cadrada

Resta 0 de -2 para obter -2.

$$\sigma _{x}^{2}=\left(-2\right)^{2}\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Calcula -2 á potencia de 2 e obtén 4.

$$\sigma _{x}^{2}=4\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Multiplica 4 e \frac{4}{9} para obter \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Multiplica 0 e 0 para obter 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Calcula 0 á potencia de 2 e obtén 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Reduce a fracción \frac{3}{9} a termos máis baixos extraendo e cancelando 3.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{1}{3}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Multiplica 0 e \frac{1}{3} para obter 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Suma \frac{16}{9} e 0 para obter \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Multiplica 1 e 9 para obter 9.

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

Calcula 9 á potencia de 2 e obtén 81.

$$\sigma _{x}^{2}=\frac{16}{9}+81\times \frac{2}{9}$$

Multiplica 81 e \frac{2}{9} para obter 18.

$$\sigma _{x}^{2}=\frac{16}{9}+18$$

Suma \frac{16}{9} e 18 para obter \frac{178}{9}.

$$\sigma _{x}^{2}=\frac{178}{9}$$

Obtén a raíz cadrada de ambos lados da ecuación.

$$\sigma _{x}=\frac{\sqrt{178}}{3} \sigma _{x}=-\frac{\sqrt{178}}{3}$$

Pasos que usan a fórmula cadrática

Resta 0 de -2 para obter -2.

$$\sigma _{x}^{2}=\left(-2\right)^{2}\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Calcula -2 á potencia de 2 e obtén 4.

$$\sigma _{x}^{2}=4\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Multiplica 4 e \frac{4}{9} para obter \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Multiplica 0 e 0 para obter 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Calcula 0 á potencia de 2 e obtén 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{3}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Reduce a fracción \frac{3}{9} a termos máis baixos extraendo e cancelando 3.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{1}{3}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Multiplica 0 e \frac{1}{3} para obter 0.

$$\sigma _{x}^{2}=\frac{16}{9}+0+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Suma \frac{16}{9} e 0 para obter \frac{16}{9}.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(1\times 9\right)^{2}\times \frac{2}{9}$$

Multiplica 1 e 9 para obter 9.

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

Calcula 9 á potencia de 2 e obtén 81.

$$\sigma _{x}^{2}=\frac{16}{9}+81\times \frac{2}{9}$$

Multiplica 81 e \frac{2}{9} para obter 18.

$$\sigma _{x}^{2}=\frac{16}{9}+18$$

Suma \frac{16}{9} e 18 para obter \frac{178}{9}.

$$\sigma _{x}^{2}=\frac{178}{9}$$

Resta \frac{178}{9} en ambos lados.

$$\sigma _{x}^{2}-\frac{178}{9}=0$$

Esta ecuación ten unha forma estándar: ax^{2}+bx+c=0. Substitúe a por 1, b por 0 e c por -\frac{178}{9} na fórmula cadrática, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\sigma _{x}=\frac{0±\sqrt{0^{2}-4\left(-\frac{178}{9}\right)}}{2}$$

Eleva 0 ao cadrado.

$$\sigma _{x}=\frac{0±\sqrt{-4\left(-\frac{178}{9}\right)}}{2}$$

Multiplica -4 por -\frac{178}{9}.

$$\sigma _{x}=\frac{0±\sqrt{\frac{712}{9}}}{2}$$

Obtén a raíz cadrada de \frac{712}{9}.

$$\sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2}$$

Agora resolve a ecuación \sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2} se ± é máis.

$$\sigma _{x}=\frac{\sqrt{178}}{3}$$

Agora resolve a ecuación \sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2} se ± é menos.

$$\sigma _{x}=-\frac{\sqrt{178}}{3}$$

A ecuación está resolta.

$$\sigma _{x}=\frac{\sqrt{178}}{3} \sigma _{x}=-\frac{\sqrt{178}}{3}$$