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Popular >

x^2+6x+9=4x^4

Solución

x^{2} + 6 x + 9 = 4 x^{4}

Solución

x = - \frac{1}{4} + i \frac{23}{4}, x = - \frac{1}{4} - i \frac{23}{4}, x = - 1, x = \frac{3}{2}

Pasos de solución

x^{2} + 6 x + 9 = 4 x^{4}

Intercambiar lados

4 x^{4} = x^{2} + 6 x + 9

Mover

9

al lado izquierdo

4 x^{4} - 9 = x^{2} + 6 x

Mover

6 x

al lado izquierdo

4 x^{4} - 9 - 6 x = x^{2}

Mover

x^{2}

al lado izquierdo

4 x^{4} - 9 - 6 x - x^{2} = 0

Escribir en la forma binómica

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

4 x^{4} - x^{2} - 6 x - 9 = 0

Factorizar

4 x^{4} - x^{2} - 6 x - 9 : (2 x^{2} + x + 3) (x + 1) (2 x - 3)

(2 x^{2} + x + 3) (x + 1) (2 x - 3) = 0

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

o

b = 0

2 x^{2} + x + 3 = 0 or x + 1 = 0 or 2 x - 3 = 0

Resolver

2 x^{2} + x + 3 = 0 : x = - \frac{1}{4} + i \frac{23}{4}, x = - \frac{1}{4} - i \frac{23}{4}

Resolver

x + 1 = 0 : x = - 1

Resolver

2 x - 3 = 0 : x = \frac{3}{2}

Las soluciones son

x = - \frac{1}{4} + i \frac{23}{4}, x = - \frac{1}{4} - i \frac{23}{4}, x = - 1, x = \frac{3}{2}

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m^{7} - 3 = 0

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1400 = 700 (1 + \frac{x}{100})^{5}

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\frac{x x ^{8}}{5} = \frac{- 2}{25}

x^{5} + 3 x^{3} - 10 x = 0

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