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

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

Solvi għal σ_x

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

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

Passi billi Ssib l-Għerq Kwadrat

Naqqas 0 minn -2 biex tikseb -2.

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

Ikkalkula -2 bil-power ta' 2 u tikseb 4.

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

Immultiplika 4 u \frac{4}{9} biex tikseb \frac{16}{9}.

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

Immultiplika 0 u 0 biex tikseb 0.

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

Ikkalkula 0 bil-power ta' 2 u tikseb 0.

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

Naqqas il-frazzjoni \frac{3}{9} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

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

Immultiplika 0 u \frac{1}{3} biex tikseb 0.

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

Żid \frac{16}{9} u 0 biex tikseb \frac{16}{9}.

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

Immultiplika 1 u 9 biex tikseb 9.

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

Ikkalkula 9 bil-power ta' 2 u tikseb 81.

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

Immultiplika 81 u \frac{2}{9} biex tikseb 18.

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

Żid \frac{16}{9} u 18 biex tikseb \frac{178}{9}.

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

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

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

Passi għall-Użu tal-Formula Kwadratika

Naqqas 0 minn -2 biex tikseb -2.

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

Ikkalkula -2 bil-power ta' 2 u tikseb 4.

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

Immultiplika 4 u \frac{4}{9} biex tikseb \frac{16}{9}.

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

Immultiplika 0 u 0 biex tikseb 0.

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

Ikkalkula 0 bil-power ta' 2 u tikseb 0.

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

Naqqas il-frazzjoni \frac{3}{9} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

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

Immultiplika 0 u \frac{1}{3} biex tikseb 0.

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

Żid \frac{16}{9} u 0 biex tikseb \frac{16}{9}.

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

Immultiplika 1 u 9 biex tikseb 9.

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

Ikkalkula 9 bil-power ta' 2 u tikseb 81.

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

Immultiplika 81 u \frac{2}{9} biex tikseb 18.

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

Żid \frac{16}{9} u 18 biex tikseb \frac{178}{9}.

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

Naqqas \frac{178}{9} miż-żewġ naħat.

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

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 1 għal a, 0 għal b, u -\frac{178}{9} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Ikkwadra 0.

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

Immultiplika -4 b'-\frac{178}{9}.

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

Ħu l-għerq kwadrat ta' \frac{712}{9}.

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

Issa solvi l-ekwazzjoni \sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2} fejn ± hija plus.

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

Issa solvi l-ekwazzjoni \sigma _{x}=\frac{0±\frac{2\sqrt{178}}{3}}{2} fejn ± hija minus.

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

L-ekwazzjoni issa solvuta.

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