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(3-x)/(1000)=(4010)/(21)(3-x-0.7)^2

Solución

\frac{3 - x}{1000} = \frac{40 \cdot 10}{2 \cdot 1} (3 - x - 0.7)^{2}

x = \frac{919999 + 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}, x = \frac{919999 - 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}

Notación decimal

x = 2.30186 \dots, x = 2.29812 \dots

Pasos de solución

\frac{3 - x}{1000} = \frac{40 \cdot 10}{2 \cdot 1} (3 - x - 0.7)^{2}

Encontrar el mínimo común múltiplo de

1000, 2 : 1000

Multiplicar por el mínimo común múltiplo=

1000

\frac{3 - x}{1000} \cdot 1000 = \frac{40 \cdot 10}{2 \cdot 1} (3 - x - 0.7)^{2} \cdot 1000

Simplificar

3 - x = 200000 (- x + 2.3)^{2}

Desarrollar

200000 (- x + 2.3)^{2} : 200000 x^{2} - 920000 x + 1058000

3 - x = 200000 x^{2} - 920000 x + 1058000

Intercambiar lados

200000 x^{2} - 920000 x + 1058000 = 3 - x

Mover

x

al lado izquierdo

200000 x^{2} - 919999 x + 1058000 = 3

Mover

3

al lado izquierdo

200000 x^{2} - 919999 x + 1057997 = 0

Dividir ambos lados entre

200000

\frac{200000 x ^{2}}{200000} - \frac{919999 x}{200000} + \frac{1057997}{200000} = \frac{0}{200000}

Escribir en la forma binómica

a x^{2} + b x + c = 0

x^{2} - \frac{919999 x}{200000} + \frac{1057997}{200000} = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

x_{1, 2} = \frac{- ( - \frac{919999}{200000} ) \pm ( - \frac{919999}{200000} ) ^{2} - 4 \cdot 1 \cdot \frac{1057997}{200000}}{2 \cdot 1}

(- \frac{919999}{200000})^{2} - 4 \cdot 1 \cdot \frac{1057997}{200000} = \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}

x_{1, 2} = \frac{- ( - \frac{919999}{200000} ) \pm \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1}

Separar las soluciones

x_{1} = \frac{- ( - \frac{919999}{200000} ) + \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1}, x_{2} = \frac{- ( - \frac{919999}{200000} ) - \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1}

x = \frac{- ( - \frac{919999}{200000} ) + \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1} : \frac{919999 + 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}

x = \frac{- ( - \frac{919999}{200000} ) - \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1} : \frac{919999 - 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}

Las soluciones a la ecuación de segundo grado son:

x = \frac{919999 + 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}, x = \frac{919999 - 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}

- 5 x^{2} + 40 x - 40 = 0

p^{2} - 3 p - 18 = 0

m^{2} + 4 m + 20 = 0

2 = y^{2}

3 x (5 x - 6) = 4 - 2 x