(m-1)x^2-(m^2+7m-5)x+5m-9=0

Lösung

(m - 1) x^{2} - (m^{2} + 7 m - 5) x + 5 m - 9 = 0

x = \frac{m ^{2} + 7 m - 5 + m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}, x = \frac{m ^{2} + 7 m - 5 - m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}; m \neq = 1

Schritte zur Lösung

(m - 1) x^{2} - (m^{2} + 7 m - 5) x + 5 m - 9 = 0

Schreibe

(m - 1) x^{2} - (m^{2} + 7 m - 5) x + 5 m - 9

um:

m x^{2} - x^{2} - m^{2} x - 7 m x + 5 x + 5 m - 9

m x^{2} - x^{2} - m^{2} x - 7 m x + 5 x + 5 m - 9 = 0

Schreibe in der Standard Form

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

(m - 1) x^{2} + (- m^{2} - 7 m + 5) x + 5 m - 9 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - m ^{2} - 7 m + 5 ) \pm ( - m ^{2} - 7 m + 5 ) ^{2} - 4 ( m - 1 ) ( 5 m - 9 )}{2 ( m - 1 )}

Vereinfache

(- m^{2} - 7 m + 5)^{2} - 4 (m - 1) (5 m - 9) : m^{4} + 14 m^{3} + 19 m^{2} - 14 m - 11

x_{1, 2} = \frac{- ( - m ^{2} - 7 m + 5 ) \pm m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}; m \neq = 1

Trenne die Lösungen

x_{1} = \frac{- ( - m ^{2} - 7 m + 5 ) + m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}, x_{2} = \frac{- ( - m ^{2} - 7 m + 5 ) - m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}

x = \frac{- ( - m ^{2} - 7 m + 5 ) + m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )} : \frac{m ^{2} + 7 m - 5 + m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}

x = \frac{- ( - m ^{2} - 7 m + 5 ) - m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )} : \frac{m ^{2} + 7 m - 5 - m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{m ^{2} + 7 m - 5 + m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}, x = \frac{m ^{2} + 7 m - 5 - m ^{4} + 14 m ^{3} + 19 m ^{2} - 14 m - 11}{2 ( m - 1 )}; m \neq = 1

3 x^{2} - 3 x + \frac{1}{2} = 0

3 w^{2} + w + 8 = 6

(x - 2)^{2} = - 8 (x - 2)

n^{2} + 12 n + 108 = 12

- (1 - t)^{2} = - 25