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Beliebt Algebra >

a(x-11)(x+a)=x^2+0x-11a

Lösung

a (x - 11) (x + a) = x^{2} + 0 x - 11 a

Lösung

x = \frac{- a ^{2} + 11 a + a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}, x = \frac{- a ^{2} + 11 a - a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}; a \neq = 1

Schritte zur Lösung

a (x - 11) (x + a) = x^{2} + 0 \cdot x - 11 a

Schreibe

a (x - 11) (x + a)

um:

a x^{2} + a^{2} x - 11 a x - 11 a^{2}

Schreibe

x^{2} + 0 \cdot x - 11 a

um:

x^{2} - 11 a

a x^{2} + a^{2} x - 11 a x - 11 a^{2} = x^{2} - 11 a

Verschiebe

11 a

auf die linke Seite

a x^{2} + a^{2} x - 11 a x - 11 a^{2} + 11 a = x^{2}

Verschiebe

x^{2}

auf die linke Seite

a x^{2} + a^{2} x - 11 a x - 11 a^{2} + 11 a - x^{2} = 0

Schreibe in der Standard Form

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

(a - 1) x^{2} + (a^{2} - 11 a) x - 11 a^{2} + 11 a = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( a ^{2} - 11 a ) \pm ( a ^{2} - 11 a ) ^{2} - 4 ( a - 1 ) ( - 11 a ^{2} + 11 a )}{2 ( a - 1 )}

Vereinfache

(a^{2} - 11 a)^{2} - 4 (a - 1) (- 11 a^{2} + 11 a) : a^{4} + 22 a^{3} + 33 a^{2} + 44 a

x_{1, 2} = \frac{- ( a ^{2} - 11 a ) \pm a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}; a \neq = 1

Trenne die Lösungen

x_{1} = \frac{- ( a ^{2} - 11 a ) + a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}, x_{2} = \frac{- ( a ^{2} - 11 a ) - a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}

x = \frac{- ( a ^{2} - 11 a ) + a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )} : \frac{- a ^{2} + 11 a + a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}

x = \frac{- ( a ^{2} - 11 a ) - a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )} : \frac{- a ^{2} + 11 a - a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- a ^{2} + 11 a + a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}, x = \frac{- a ^{2} + 11 a - a ^{4} + 22 a ^{3} + 33 a ^{2} + 44 a}{2 ( a - 1 )}; a \neq = 1

Graph

Beliebte Beispiele

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

(x + 5)^{2} + 12 = 76

2 x^{2} + 6 + 4 = 0

solvefor x,z^2=y^2+x^2

so l v e f or x, z^{2} = y^{2} + x^{2}

12 x^{2} - 5 = - 3