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Beliebt Algebra >

(a-b)*x^2+(b+c-a)x-c=0

Lösung

(a - b) \cdot x^{2} + (b + c - a) x - c = 0

Lösung

x = \frac{- b - c + a + c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}, x = \frac{- b - c + a - c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}; a - b \neq = 0

Schritte zur Lösung

(a - b) x^{2} + (b + c - a) x - c = 0

Löse mit der quadratischen Formel

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

Vereinfache

(b + c - a)^{2} - 4 (a - b) (- c) : c^{2} + 2 a c - 2 b c + a^{2} + b^{2} - 2 ab

x_{1, 2} = \frac{- ( b + c - a ) \pm c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}; a - b \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( b + c - a ) + c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}, x_{2} = \frac{- ( b + c - a ) - c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}

x = \frac{- ( b + c - a ) + c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )} : \frac{- b - c + a + c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}

x = \frac{- ( b + c - a ) - c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )} : \frac{- b - c + a - c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- b - c + a + c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}, x = \frac{- b - c + a - c ^{2} + 2 a c - 2 b c + a ^{2} + b ^{2} - 2 ab}{2 ( a - b )}; a - b \neq = 0

Graph

Beliebte Beispiele

(3/5 x-2/3)^2= 5/6

(\frac{3}{5} x - \frac{2}{3})^{2} = \frac{5}{6}

solvefor u,1+d^2u^2=(1+(d^2)/2)^2

so l v e f or u, 1 + d^{2} u^{2} = (1 + \frac{d ^{2}}{2})^{2}

solvefor x,(6x+3y+2z)^2=49

so l v e f or x, (6 x + 3 y + 2 z)^{2} = 49

x^2+(98-m)^2=41

x^{2} + (98 - m)^{2} = 41

solvefor x,(x+y)^2=4

so l v e f or x, (x + y)^{2} = 4