Resolver left(1.05^4+1.05^3+1.05^2+1.05+1.05^5right)x=5

$$\left( { 1.05 }^{ 4 } + { 1.05 }^{ 3 } + { 1.05 }^{ 2 } +1.05+ { 1.05 }^{ 5 } \right) x = 5$$

Resolver x

$$x=\frac{16000000}{18566121}\approx 0.861784753$$

Pasos para resolver unha ecuación lineal

Calcula 1.05 á potencia de 4 e obtén 1.21550625.

$$\left(1.21550625+1.05^{3}+1.05^{2}+1.05+1.05^{5}\right)x=5$$

Calcula 1.05 á potencia de 3 e obtén 1.157625.

$$\left(1.21550625+1.157625+1.05^{2}+1.05+1.05^{5}\right)x=5$$

Suma 1.21550625 e 1.157625 para obter 2.37313125.

$$\left(2.37313125+1.05^{2}+1.05+1.05^{5}\right)x=5$$

Calcula 1.05 á potencia de 2 e obtén 1.1025.

$$\left(2.37313125+1.1025+1.05+1.05^{5}\right)x=5$$

Suma 2.37313125 e 1.1025 para obter 3.47563125.

$$\left(3.47563125+1.05+1.05^{5}\right)x=5$$

Suma 3.47563125 e 1.05 para obter 4.52563125.

$$\left(4.52563125+1.05^{5}\right)x=5$$

Calcula 1.05 á potencia de 5 e obtén 1.2762815625.

$$\left(4.52563125+1.2762815625\right)x=5$$

Suma 4.52563125 e 1.2762815625 para obter 5.8019128125.

$$5.8019128125x=5$$

Divide ambos lados entre 5.8019128125.

$$x=\frac{5}{5.8019128125}$$

Expande \frac{5}{5.8019128125} multiplicando o numerador e o denominador por 10000000000.

$$x=\frac{50000000000}{58019128125}$$

Reduce a fracción \frac{50000000000}{58019128125} a termos máis baixos extraendo e cancelando 3125.

$$x=\frac{16000000}{18566121}$$