-5t^2+(20+6e^{-4})t-(16+15e^{-4})=0

Lösung

- 5 t^{2} + (20 + 6 e^{- 4}) t - (16 + 15 e^{- 4}) = 0

t = \frac{6 + 20 e ^{4} - e ^{4} 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{10 e ^{4}}, t = \frac{6 + 20 e ^{4} + e ^{4} 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{10 e ^{4}}

Dezimale

t = 1.12265 \dots, t = 2.89932 \dots

Schritte zur Lösung

- 5 t^{2} + (20 + 6 e^{- 4}) t - (16 + 15 e^{- 4}) = 0

Schreibe

- 5 t^{2} + (20 + 6 e^{- 4}) t - (16 + 15 e^{- 4})

um:

- 5 t^{2} + \frac{20 e ^{4} + 6}{e ^{4}} t - 16 - \frac{15}{e ^{4}}

- 5 t^{2} + \frac{20 e ^{4} + 6}{e ^{4}} t - 16 - \frac{15}{e ^{4}} = 0

Schreibe in der Standard Form

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

- 5 t^{2} + (20 + \frac{6}{e ^{4}}) t - \frac{15}{e ^{4}} - 16 = 0

Löse mit der quadratischen Formel

t_{1, 2} = \frac{- ( 20 + \frac{6}{e ^{4}} ) \pm ( 20 + \frac{6}{e ^{4}} ) ^{2} - 4 ( - 5 ) ( - \frac{15}{e ^{4}} - 16 )}{2 ( - 5 )}

(20 + \frac{6}{e ^{4}})^{2} - 4 (- 5) (- \frac{15}{e ^{4}} - 16) = 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}

t_{1, 2} = \frac{- ( 20 + \frac{6}{e ^{4}} ) \pm 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{2 ( - 5 )}

Trenne die Lösungen

t_{1} = \frac{- ( 20 + \frac{6}{e ^{4}} ) + 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{2 ( - 5 )}, t_{2} = \frac{- ( 20 + \frac{6}{e ^{4}} ) - 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{2 ( - 5 )}

t = \frac{- ( 20 + \frac{6}{e ^{4}} ) + 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{2 ( - 5 )} : \frac{6 + 20 e ^{4} - e ^{4} 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{10 e ^{4}}

t = \frac{- ( 20 + \frac{6}{e ^{4}} ) - 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{2 ( - 5 )} : \frac{6 + 20 e ^{4} + e ^{4} 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{10 e ^{4}}

Die Lösungen für die quadratische Gleichung sind:

t = \frac{6 + 20 e ^{4} - e ^{4} 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{10 e ^{4}}, t = \frac{6 + 20 e ^{4} + e ^{4} 80 + \frac{36}{e ^{8}} - \frac{60}{e ^{4}}}{10 e ^{4}}

A^{2} = A

- 2 y = 4 y^{2}

1 x^{2} - 6 x + 8 = 0

(x + 6) (x + 4) = 2 x^{2}

(z - 4) (z - 6) = 0