-(550x^2)/2+(2000(x-4)^2)/2+3200=0

Solución

- \frac{550 x ^{2}}{2} + \frac{2000 ( x - 4 ) ^{2}}{2} + 3200 = 0

x = \frac{16 ( 10 + 13 )}{29}, x = \frac{16 ( 10 - 13 )}{29}

Notación decimal

x = 7.50651 \dots, x = 3.52797 \dots

Pasos de solución

- \frac{550 x ^{2}}{2} + \frac{2000 ( x - 4 ) ^{2}}{2} + 3200 = 0

Multiplicar ambos lados por

2

- 550 x^{2} + 2000 (x - 4)^{2} + 6400 = 0

Desarrollar

- 550 x^{2} + 2000 (x - 4)^{2} + 6400 : 1450 x^{2} - 16000 x + 38400

1450 x^{2} - 16000 x + 38400 = 0

Dividir ambos lados entre

1450

\frac{1450 x ^{2}}{1450} - \frac{16000 x}{1450} + \frac{38400}{1450} = \frac{0}{1450}

Escribir en la forma binómica

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

x^{2} - \frac{320 x}{29} + \frac{768}{29} = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

x_{1, 2} = \frac{- ( - \frac{320}{29} ) \pm ( - \frac{320}{29} ) ^{2} - 4 \cdot 1 \cdot \frac{768}{29}}{2 \cdot 1}

(- \frac{320}{29})^{2} - 4 \cdot 1 \cdot \frac{768}{29} = \frac{32 13}{29}

x_{1, 2} = \frac{- ( - \frac{320}{29} ) \pm \frac{32 13}{29}}{2 \cdot 1}

Separar las soluciones

x_{1} = \frac{- ( - \frac{320}{29} ) + \frac{32 13}{29}}{2 \cdot 1}, x_{2} = \frac{- ( - \frac{320}{29} ) - \frac{32 13}{29}}{2 \cdot 1}

x = \frac{- ( - \frac{320}{29} ) + \frac{32 13}{29}}{2 \cdot 1} : \frac{16 ( 10 + 13 )}{29}

x = \frac{- ( - \frac{320}{29} ) - \frac{32 13}{29}}{2 \cdot 1} : \frac{16 ( 10 - 13 )}{29}

Las soluciones a la ecuación de segundo grado son:

x = \frac{16 ( 10 + 13 )}{29}, x = \frac{16 ( 10 - 13 )}{29}

- 7 a^{5} n^{2} = 2

x (x - 15) = 100

x, x^{2} + 4 x y + 4 y^{2} - 3 x + 4 y - 10 = 0

x (x + 1) - (4 - x) (x + 1) = 6 (4 - x)

y, z^{2} = x^{2} + y^{2}