(m-1)x^2+2(m-1)x-1=0

Lösung

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

x = \frac{- m + 1 + m ( m - 1 )}{m - 1}, x = \frac{- m + 1 - m ( m - 1 )}{m - 1}; m \neq = 1

Schritte zur Lösung

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

Schreibe

(m - 1) x^{2} + 2 (m - 1) x - 1

um:

m x^{2} - x^{2} + 2 m x - 2 x - 1

m x^{2} - x^{2} + 2 m x - 2 x - 1 = 0

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 2 m - 2 ) \pm ( 2 m - 2 ) ^{2} - 4 ( m - 1 ) ( - 1 )}{2 ( m - 1 )}

Vereinfache

(2 m - 2)^{2} - 4 (m - 1) (- 1) : 2 m (m - 1)

x_{1, 2} = \frac{- ( 2 m - 2 ) \pm 2 m ( m - 1 )}{2 ( m - 1 )}; m \neq = 1

Trenne die Lösungen

x_{1} = \frac{- ( 2 m - 2 ) + 2 m ( m - 1 )}{2 ( m - 1 )}, x_{2} = \frac{- ( 2 m - 2 ) - 2 m ( m - 1 )}{2 ( m - 1 )}

x = \frac{- ( 2 m - 2 ) + 2 m ( m - 1 )}{2 ( m - 1 )} : \frac{- m + 1 + m ( m - 1 )}{m - 1}

x = \frac{- ( 2 m - 2 ) - 2 m ( m - 1 )}{2 ( m - 1 )} : \frac{- m + 1 - m ( m - 1 )}{m - 1}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- m + 1 + m ( m - 1 )}{m - 1}, x = \frac{- m + 1 - m ( m - 1 )}{m - 1}; m \neq = 1

p^{2} - 2 p + 1 = 0

x^{2} = - x + 6

so l v e f or x, 3 x^{2} - 2 x - 3 = 0

2 x^{2} + 5 = 8 x

2 x^{2} + 5 = 21