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

Lösung

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

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

Schritte zur Lösung

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

Schreibe

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

um:

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

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

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

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

Vereinfache

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

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

Trenne die Lösungen

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

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

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

Die Lösungen für die quadratische Gleichung sind:

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

(2 x + 5)^{2} = 16

x^{2} + 6 x + 20 = - \frac{1}{2} x^{2} - 4 x + 196

- 4 x^{2} - 4 = 0

25 x^{2} + 5 = 0

x (x + 12) = 12