x^2+5.110^{-4}x-(0.00015.1*10^{-4})=0

Lösung

x^{2} + 5.1 \cdot 1 0^{- 4} x - (0.0001 \cdot 5.1 \cdot 1 0^{- 4}) = 0

x = \frac{- 5.1 + 46.41}{20000}, x = \frac{- 5.1 - 46.41}{20000}

Dezimale

x = 0.00008 \dots, x = - 0.00059 \dots

Schritte zur Lösung

x^{2} + 5.1 \cdot 1 0^{- 4} x - (0.0001 \cdot 5.1 \cdot 1 0^{- 4}) = 0

Schreibe

x^{2} + 5.1 \cdot 1 0^{- 4} x - (0.0001 \cdot 5.1 \cdot 1 0^{- 4})

um:

x^{2} + \frac{5.1}{10000} x - \frac{0.00051}{10000}

x^{2} + \frac{5.1}{10000} x - \frac{0.00051}{10000} = 0

Schreibe in der Standard Form

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

x^{2} + \frac{5.1 x}{10000} - \frac{0.00051}{10000} = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- \frac{5.1}{10000} \pm ( \frac{5.1}{10000} ) ^{2} - 4 \cdot 1 \cdot ( - \frac{0.00051}{10000} )}{2 \cdot 1}

(\frac{5.1}{10000})^{2} - 4 \cdot 1 \cdot (- \frac{0.00051}{10000}) = \frac{46.41}{10000}

x_{1, 2} = \frac{- \frac{5.1}{10000} \pm \frac{46.41}{10000}}{2 \cdot 1}

Trenne die Lösungen

x_{1} = \frac{- \frac{5.1}{10000} + \frac{46.41}{10000}}{2 \cdot 1}, x_{2} = \frac{- \frac{5.1}{10000} - \frac{46.41}{10000}}{2 \cdot 1}

x = \frac{- \frac{5.1}{10000} + \frac{46.41}{10000}}{2 \cdot 1} : \frac{- 5.1 + 46.41}{20000}

x = \frac{- \frac{5.1}{10000} - \frac{46.41}{10000}}{2 \cdot 1} : \frac{- 5.1 - 46.41}{20000}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 5.1 + 46.41}{20000}, x = \frac{- 5.1 - 46.41}{20000}

2 s^{2} - 21 s + 49 = 0

5 x^{2} - 25 x + 3 = 0

n^{2} - n - 240 = 0

z^{2} + 14 z + 45 = 0

co m pl e t es q u a re x^{2} - 2 x