mx^2-2(m-1)x+3m-1=0

Lösung

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

x = \frac{m - 1 + - 2 m ^{2} - m + 1}{m}, x = \frac{m - 1 - - 2 m ^{2} - m + 1}{m}; m \neq = 0

Schritte zur Lösung

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

Schreibe

m x^{2} - 2 (m - 1) x + 3 m - 1

um:

m x^{2} - 2 m x + 2 x + 3 m - 1

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

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 2 m + 2 ) \pm ( - 2 m + 2 ) ^{2} - 4 m ( 3 m - 1 )}{2 m}

Vereinfache

(- 2 m + 2)^{2} - 4 m (3 m - 1) : 2 - 2 m^{2} - m + 1

x_{1, 2} = \frac{- ( - 2 m + 2 ) \pm 2 - 2 m ^{2} - m + 1}{2 m}; m \neq = 0

Trenne die Lösungen

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

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

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

Die Lösungen für die quadratische Gleichung sind:

x = \frac{m - 1 + - 2 m ^{2} - m + 1}{m}, x = \frac{m - 1 - - 2 m ^{2} - m + 1}{m}; m \neq = 0

X^{2} - 2 X = 0

8 y^{2} - 24 y = 3

x^{2} - 6 = 2 x

1 5^{2} + 1 2^{2} = x^{2}

(x - 5) (4 x + 2) = - 3