(m+1)x^2-sqrt(2)x+2(m-1)=0

Lösung

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

x = \frac{2 + - 8 m ^{2} + 10}{2 ( m + 1 )}, x = \frac{2 - - 8 m ^{2} + 10}{2 ( m + 1 )}; m \neq = - 1

Schritte zur Lösung

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

Schreibe

(m + 1) x^{2} - 2 x + 2 (m - 1)

um:

m x^{2} + x^{2} - 2 x + 2 m - 2

m x^{2} + x^{2} - 2 x + 2 m - 2 = 0

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

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

Vereinfache

(- 2)^{2} - 4 (m + 1) (2 m - 2) : - 8 m^{2} + 10

x_{1, 2} = \frac{- ( - 2 ) \pm - 8 m ^{2} + 10}{2 ( m + 1 )}; m \neq = - 1

Trenne die Lösungen

x_{1} = \frac{- ( - 2 ) + - 8 m ^{2} + 10}{2 ( m + 1 )}, x_{2} = \frac{- ( - 2 ) - - 8 m ^{2} + 10}{2 ( m + 1 )}

x = \frac{- ( - 2 ) + - 8 m ^{2} + 10}{2 ( m + 1 )} : \frac{2 + - 8 m ^{2} + 10}{2 ( m + 1 )}

x = \frac{- ( - 2 ) - - 8 m ^{2} + 10}{2 ( m + 1 )} : \frac{2 - - 8 m ^{2} + 10}{2 ( m + 1 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{2 + - 8 m ^{2} + 10}{2 ( m + 1 )}, x = \frac{2 - - 8 m ^{2} + 10}{2 ( m + 1 )}; m \neq = - 1

co m pl e t es q u a re x^{2} - 8 x - 5

co m pl e t es q u a re x^{2} - 8 x - 2

co m pl e t es q u a re x^{2} - 8 x + 4

3 x^{2} = 15 x - 22

y^{2} + 14 y + 49 = 0