Resolver -6x=15^2*8.854*10^-12*(80*10^-3+x)*20*10^-3

$$- 6 x = 15 ^ { 2 } \cdot 8.854 \cdot 10 ^ { - 12 } \cdot ( 80 \cdot 10 ^ { - 3 } + x ) \cdot 20 \cdot 10 ^ { - 3 }$$

Resolver x

$$x=-\frac{26562}{50000000000332025}\approx -5.3124 \cdot 10^{-13}$$

Pasos para resolver unha ecuación lineal

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -12 e -3 para obter -15.

$$-6x=15^{2}\times 8.854\times 10^{-15}\left(80\times 10^{-3}+x\right)\times 20$$

Calcula 15 á potencia de 2 e obtén 225.

$$-6x=225\times 8.854\times 10^{-15}\left(80\times 10^{-3}+x\right)\times 20$$

Multiplica 225 e 8.854 para obter 1992.15.

$$-6x=1992.15\times 10^{-15}\left(80\times 10^{-3}+x\right)\times 20$$

Calcula 10 á potencia de -15 e obtén \frac{1}{1000000000000000}.

$$-6x=1992.15\times \frac{1}{1000000000000000}\left(80\times 10^{-3}+x\right)\times 20$$

Multiplica 1992.15 e \frac{1}{1000000000000000} para obter \frac{39843}{20000000000000000}.

$$-6x=\frac{39843}{20000000000000000}\left(80\times 10^{-3}+x\right)\times 20$$

Calcula 10 á potencia de -3 e obtén \frac{1}{1000}.

$$-6x=\frac{39843}{20000000000000000}\left(80\times \frac{1}{1000}+x\right)\times 20$$

Multiplica 80 e \frac{1}{1000} para obter \frac{2}{25}.

$$-6x=\frac{39843}{20000000000000000}\left(\frac{2}{25}+x\right)\times 20$$

Multiplica \frac{39843}{20000000000000000} e 20 para obter \frac{39843}{1000000000000000}.

$$-6x=\frac{39843}{1000000000000000}\left(\frac{2}{25}+x\right)$$

Usa a propiedade distributiva para multiplicar \frac{39843}{1000000000000000} por \frac{2}{25}+x.

$$-6x=\frac{39843}{12500000000000000}+\frac{39843}{1000000000000000}x$$

Resta \frac{39843}{1000000000000000}x en ambos lados.

$$-6x-\frac{39843}{1000000000000000}x=\frac{39843}{12500000000000000}$$

Combina -6x e -\frac{39843}{1000000000000000}x para obter -\frac{6000000000039843}{1000000000000000}x.

$$-\frac{6000000000039843}{1000000000000000}x=\frac{39843}{12500000000000000}$$

Multiplica ambos lados por -\frac{1000000000000000}{6000000000039843}, o recíproco de -\frac{6000000000039843}{1000000000000000}.

$$x=\frac{39843}{12500000000000000}\left(-\frac{1000000000000000}{6000000000039843}\right)$$

Multiplica \frac{39843}{12500000000000000} e -\frac{1000000000000000}{6000000000039843} para obter -\frac{26562}{50000000000332025}.

$$x=-\frac{26562}{50000000000332025}$$