solvefor x,-kx^2+px-k=0

Lösung

löse nach

x, - k x^{2} + p x - k = 0

x = - \frac{- p + p ^{2} - 4 k ^{2}}{2 k}, x = - \frac{- p - p ^{2} - 4 k ^{2}}{2 k}; k \neq = 0

Schritte zur Lösung

- k x^{2} + p x - k = 0

Löse mit der quadratischen Formel

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

Vereinfache

p^{2} - 4 (- k) (- k) : p^{2} - 4 k^{2}

x_{1, 2} = \frac{- p \pm p ^{2} - 4 k ^{2}}{2 ( - k )}; k \neq = 0

Trenne die Lösungen

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

x = \frac{- p + p ^{2} - 4 k ^{2}}{2 ( - k )} : - \frac{- p + p ^{2} - 4 k ^{2}}{2 k}

x = \frac{- p - p ^{2} - 4 k ^{2}}{2 ( - k )} : - \frac{- p - p ^{2} - 4 k ^{2}}{2 k}

Die Lösungen für die quadratische Gleichung sind:

x = - \frac{- p + p ^{2} - 4 k ^{2}}{2 k}, x = - \frac{- p - p ^{2} - 4 k ^{2}}{2 k}; k \neq = 0

2 x^{2} - 5 x + 13 = 0

(1 - 2 x) (1 + 2 x) = 3 x

\frac{3 x}{8} - \frac{x ^{2}}{8} = 0

x^{2} + 36 x + 332 = 0

13 x^{2} - 27 = 0