(2k+2)x^2+(4-4k)x+k-2=0

Lösung

(2 k + 2) x^{2} + (4 - 4 k) x + k - 2 = 0

x = \frac{- 4 + 4 k + 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}, x = \frac{- 4 + 4 k - 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}; k \neq = - 1

Schritte zur Lösung

(2 k + 2) x^{2} + (4 - 4 k) x + k - 2 = 0

Löse mit der quadratischen Formel

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

Vereinfache

(4 - 4 k)^{2} - 4 (2 k + 2) (k - 2) : 8 k^{2} - 24 k + 32

x_{1, 2} = \frac{- ( 4 - 4 k ) \pm 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}; k \neq = - 1

Trenne die Lösungen

x_{1} = \frac{- ( 4 - 4 k ) + 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}, x_{2} = \frac{- ( 4 - 4 k ) - 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}

x = \frac{- ( 4 - 4 k ) + 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )} : \frac{- 4 + 4 k + 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}

x = \frac{- ( 4 - 4 k ) - 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )} : \frac{- 4 + 4 k - 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 4 + 4 k + 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}, x = \frac{- 4 + 4 k - 8 k ^{2} - 24 k + 32}{2 ( 2 k + 2 )}; k \neq = - 1

2 d^{2} - 8 d + 19 = 6 d

12 x^{2} + 12 x - 6 = 0

2 x^{2} - 5 x = - 5

x^{2} - 5 x + 9 = 3

co m pl e t es q u a re x^{2} + 4 x - 3