(k-1)x^2+(k+4)x+25=0,k\ne 1

Lösung

(k - 1) x^{2} + (k + 4) x + 25 = 0, k \neq = 1

x = \frac{- k - 4 + k ^{2} - 92 k + 116}{2 ( k - 1 )}, x = \frac{- k - 4 - k ^{2} - 92 k + 116}{2 ( k - 1 )}; k \neq = 1

Schritte zur Lösung

(k - 1) x^{2} + (k + 4) x + 25 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( k + 4 ) \pm ( k + 4 ) ^{2} - 4 ( k - 1 ) \cdot 25}{2 ( k - 1 )}

Vereinfache

(k + 4)^{2} - 4 (k - 1) \cdot 25 : k^{2} - 92 k + 116

x_{1, 2} = \frac{- ( k + 4 ) \pm k ^{2} - 92 k + 116}{2 ( k - 1 )}; k \neq = 1

Trenne die Lösungen

x_{1} = \frac{- ( k + 4 ) + k ^{2} - 92 k + 116}{2 ( k - 1 )}, x_{2} = \frac{- ( k + 4 ) - k ^{2} - 92 k + 116}{2 ( k - 1 )}

x = \frac{- ( k + 4 ) + k ^{2} - 92 k + 116}{2 ( k - 1 )} : \frac{- k - 4 + k ^{2} - 92 k + 116}{2 ( k - 1 )}

x = \frac{- ( k + 4 ) - k ^{2} - 92 k + 116}{2 ( k - 1 )} : \frac{- k - 4 - k ^{2} - 92 k + 116}{2 ( k - 1 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- k - 4 + k ^{2} - 92 k + 116}{2 ( k - 1 )}, x = \frac{- k - 4 - k ^{2} - 92 k + 116}{2 ( k - 1 )}; k \neq = 1

5 x^{2} - 26 x - 24 = 0

0 = x^{2} + x + 4

- 2 x^{2} = 4 x

x + 7 + 2 x - 3 = x^{2}

(3 - x)^{2} + 4 - 2 (3 - x) = x