Resolver 50*10^{3}=(9*10^9)(80*10^66)(-6*10^-6)/r^2

$$50 \times 10 ^ { 3 } = \frac { ( 9 \times 10 ^ { 9 } ) ( 80 \times 10 ^ { 66 } ) ( - 6 \times 10 ^ { - 6 } ) } { r ^ { 2 } }$$

Resolver r

$$r=-2400000000000000000000000000000000\sqrt{15}i\approx -0-9.295160031 \cdot 10^{33}i$$

$$r=2400000000000000000000000000000000\sqrt{15}i\approx 9.295160031 \cdot 10^{33}i$$

Pasos para obter a raíz cadrada

A variable r non pode ser igual a 0 porque a división entre cero non está definida. Multiplica ambos lados da ecuación por r^{2}.

$$50\times 10^{3}r^{2}=9\times 10^{9}\times 80\times 10^{66}\left(-6\right)\times 10^{-6}$$

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma 9 e 66 para obter 75.

$$50\times 10^{3}r^{2}=9\times 10^{75}\times 80\left(-6\right)\times 10^{-6}$$

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma 75 e -6 para obter 69.

$$50\times 10^{3}r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Calcula 10 á potencia de 3 e obtén 1000.

$$50\times 1000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Multiplica 50 e 1000 para obter 50000.

$$50000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Calcula 10 á potencia de 69 e obtén 1000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=9\times 1000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

Multiplica 9 e 1000000000000000000000000000000000000000000000000000000000000000000000 para obter 9000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=9000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

Multiplica 9000000000000000000000000000000000000000000000000000000000000000000000 e 80 para obter 720000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=720000000000000000000000000000000000000000000000000000000000000000000000\left(-6\right)$$

Multiplica 720000000000000000000000000000000000000000000000000000000000000000000000 e -6 para obter -4320000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=-4320000000000000000000000000000000000000000000000000000000000000000000000$$

Divide ambos lados entre 50000.

$$r^{2}=\frac{-4320000000000000000000000000000000000000000000000000000000000000000000000}{50000}$$

Divide -4320000000000000000000000000000000000000000000000000000000000000000000000 entre 50000 para obter -86400000000000000000000000000000000000000000000000000000000000000000.

$$r^{2}=-86400000000000000000000000000000000000000000000000000000000000000000$$

A ecuación está resolta.

$$r=2400000000000000000000000000000000\sqrt{15}i r=-2400000000000000000000000000000000\sqrt{15}i$$

Pasos que usan a fórmula cadrática

A variable r non pode ser igual a 0 porque a división entre cero non está definida. Multiplica ambos lados da ecuación por r^{2}.

$$50\times 10^{3}r^{2}=9\times 10^{9}\times 80\times 10^{66}\left(-6\right)\times 10^{-6}$$

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma 9 e 66 para obter 75.

$$50\times 10^{3}r^{2}=9\times 10^{75}\times 80\left(-6\right)\times 10^{-6}$$

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma 75 e -6 para obter 69.

$$50\times 10^{3}r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Calcula 10 á potencia de 3 e obtén 1000.

$$50\times 1000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Multiplica 50 e 1000 para obter 50000.

$$50000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

Calcula 10 á potencia de 69 e obtén 1000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=9\times 1000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

Multiplica 9 e 1000000000000000000000000000000000000000000000000000000000000000000000 para obter 9000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=9000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

Multiplica 9000000000000000000000000000000000000000000000000000000000000000000000 e 80 para obter 720000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=720000000000000000000000000000000000000000000000000000000000000000000000\left(-6\right)$$

Multiplica 720000000000000000000000000000000000000000000000000000000000000000000000 e -6 para obter -4320000000000000000000000000000000000000000000000000000000000000000000000.

$$50000r^{2}=-4320000000000000000000000000000000000000000000000000000000000000000000000$$

Engadir 4320000000000000000000000000000000000000000000000000000000000000000000000 en ambos lados.

$$50000r^{2}+4320000000000000000000000000000000000000000000000000000000000000000000000=0$$

Esta ecuación ten unha forma estándar: ax^{2}+bx+c=0. Substitúe a por 50000, b por 0 e c por 4320000000000000000000000000000000000000000000000000000000000000000000000 na fórmula cadrática, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 50000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

Eleva 0 ao cadrado.

$$r=\frac{0±\sqrt{-4\times 50000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

Multiplica -4 por 50000.

$$r=\frac{0±\sqrt{-200000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

Multiplica -200000 por 4320000000000000000000000000000000000000000000000000000000000000000000000.

$$r=\frac{0±\sqrt{-864000000000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

Obtén a raíz cadrada de -864000000000000000000000000000000000000000000000000000000000000000000000000000.

$$r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{2\times 50000}$$

Multiplica 2 por 50000.

$$r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000}$$

Agora resolve a ecuación r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} se ± é máis.

$$r=2400000000000000000000000000000000\sqrt{15}i$$

Agora resolve a ecuación r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} se ± é menos.

$$r=-2400000000000000000000000000000000\sqrt{15}i$$

A ecuación está resolta.

$$r=2400000000000000000000000000000000\sqrt{15}i r=-2400000000000000000000000000000000\sqrt{15}i$$