(k-12)x^2+2(k-12)x+2=0

Lösung

(k - 12) x^{2} + 2 (k - 12) x + 2 = 0

x = \frac{- k + 12 + k ^{2} - 26 k + 168}{k - 12}, x = \frac{- k + 12 - k ^{2} - 26 k + 168}{k - 12}; k \neq = 12

Schritte zur Lösung

(k - 12) x^{2} + 2 (k - 12) x + 2 = 0

Schreibe

(k - 12) x^{2} + 2 (k - 12) x + 2

um:

k x^{2} - 12 x^{2} + 2 k x - 24 x + 2

k x^{2} - 12 x^{2} + 2 k x - 24 x + 2 = 0

Schreibe in der Standard Form

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

(k - 12) x^{2} + (2 k - 24) x + 2 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 2 k - 24 ) \pm ( 2 k - 24 ) ^{2} - 4 ( k - 12 ) \cdot 2}{2 ( k - 12 )}

Vereinfache

(2 k - 24)^{2} - 4 (k - 12) \cdot 2 : 2 k^{2} - 26 k + 168

x_{1, 2} = \frac{- ( 2 k - 24 ) \pm 2 k ^{2} - 26 k + 168}{2 ( k - 12 )}; k \neq = 12

Trenne die Lösungen

x_{1} = \frac{- ( 2 k - 24 ) + 2 k ^{2} - 26 k + 168}{2 ( k - 12 )}, x_{2} = \frac{- ( 2 k - 24 ) - 2 k ^{2} - 26 k + 168}{2 ( k - 12 )}

x = \frac{- ( 2 k - 24 ) + 2 k ^{2} - 26 k + 168}{2 ( k - 12 )} : \frac{- k + 12 + k ^{2} - 26 k + 168}{k - 12}

x = \frac{- ( 2 k - 24 ) - 2 k ^{2} - 26 k + 168}{2 ( k - 12 )} : \frac{- k + 12 - k ^{2} - 26 k + 168}{k - 12}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- k + 12 + k ^{2} - 26 k + 168}{k - 12}, x = \frac{- k + 12 - k ^{2} - 26 k + 168}{k - 12}; k \neq = 12

\frac{3 x ^{2} - 4 x}{6} = 20 x

\frac{x ^{2} - x}{12} = 1

a^{12} x + 4 x = - 3 x^{2} + x - 5

3 x^{1} - 2 x^{2} = 4

3 x^{2} - (7 - k) \cdot x + 9 = 0