643x+4600x^2-1=0

Solución

643 x + 4600 x^{2} - 1 = 0

x = \frac{- 643 + 11 3569}{9200}, x = \frac{- 643 - 11 3569}{9200}

Notación decimal

x = 0.00153 \dots, x = - 0.14132 \dots

Pasos de solución

643 x + 4600 x^{2} - 1 = 0

Dividir ambos lados entre

4600

\frac{643 x}{4600} + \frac{4600 x ^{2}}{4600} - \frac{1}{4600} = \frac{0}{4600}

Escribir en la forma binómica

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

x^{2} + \frac{643 x}{4600} - \frac{1}{4600} = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

x_{1, 2} = \frac{- \frac{643}{4600} \pm ( \frac{643}{4600} ) ^{2} - 4 \cdot 1 \cdot ( - \frac{1}{4600} )}{2 \cdot 1}

(\frac{643}{4600})^{2} - 4 \cdot 1 \cdot (- \frac{1}{4600}) = \frac{11 3569}{4600}

x_{1, 2} = \frac{- \frac{643}{4600} \pm \frac{11 3569}{4600}}{2 \cdot 1}

Separar las soluciones

x_{1} = \frac{- \frac{643}{4600} + \frac{11 3569}{4600}}{2 \cdot 1}, x_{2} = \frac{- \frac{643}{4600} - \frac{11 3569}{4600}}{2 \cdot 1}

x = \frac{- \frac{643}{4600} + \frac{11 3569}{4600}}{2 \cdot 1} : \frac{- 643 + 11 3569}{9200}

x = \frac{- \frac{643}{4600} - \frac{11 3569}{4600}}{2 \cdot 1} : \frac{- 643 - 11 3569}{9200}

Las soluciones a la ecuación de segundo grado son:

x = \frac{- 643 + 11 3569}{9200}, x = \frac{- 643 - 11 3569}{9200}

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