0.0813600000000…+0.2431900000000…x+0.3564800000000…x^2=0

Lösung

0.0813600000000 \dots + 0.2431900000000 \dots \cdot x + 0.3564800000000 \dots \cdot x^{2} = 0

x = - \frac{0.24319 \dots}{0.71296} + i \frac{0.0568714751}{0.71296}, x = - \frac{0.24319 \dots}{0.71296} - i \frac{0.0568714751}{0.71296}

Schritte zur Lösung

0.08136 \dots + 0.24319 \dots x + 0.35648 \dots x^{2} = 0

Schreibe in der Standard Form

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

0.35648 \dots x^{2} + 0.24319 \dots x + 0.08136 \dots = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- 0.24319 \dots \pm 0.24319 \dots ^{2} - 4 \cdot 0.35648 \dots \cdot 0.08136 \dots}{2 \cdot 0.35648 \dots}

Vereinfache

0.24319 \dots^{2} - 4 \cdot 0.35648 \dots \cdot 0.08136 \dots : 0.0568714751 i

x_{1, 2} = \frac{- 0.24319 \dots \pm 0.0568714751 i}{2 \cdot 0.35648 \dots}

Trenne die Lösungen

x_{1} = \frac{- 0.24319 \dots + 0.0568714751 i}{2 \cdot 0.35648 \dots}, x_{2} = \frac{- 0.24319 \dots - 0.0568714751 i}{2 \cdot 0.35648 \dots}

x = \frac{- 0.24319 \dots + 0.0568714751 i}{2 \cdot 0.35648 \dots} : - \frac{0.24319 \dots}{0.71296} + i \frac{0.0568714751}{0.71296}

x = \frac{- 0.24319 \dots - 0.0568714751 i}{2 \cdot 0.35648 \dots} : - \frac{0.24319 \dots}{0.71296} - i \frac{0.0568714751}{0.71296}

Die Lösungen für die quadratische Gleichung sind:

x = - \frac{0.24319 \dots}{0.71296} + i \frac{0.0568714751}{0.71296}, x = - \frac{0.24319 \dots}{0.71296} - i \frac{0.0568714751}{0.71296}

x^{2} - 13 x = - 12

3 x^{2} + 1 = 0

7 x^{2} + 2 x - 9 = 0

x^{2} + 3 = x + 3

(6 - x) (3 - x) - 4 = 0