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Beliebt Algebra >

(x+2)(x-3)(x+1)(x+6)=-36

Lösung

(x + 2) (x - 3) (x + 1) (x + 6) = - 36

Lösung

x = 0, x = - 3, x = \frac{- 3 + 73}{2}, x = \frac{- 3 - 73}{2}

+1

Dezimale

x = 0, x = - 3, x = 2.77200 \dots, x = - 5.77200 \dots

Schritte zur Lösung

(x + 2) (x - 3) (x + 1) (x + 6) = - 36

Schreibe

(x + 2) (x - 3) (x + 1) (x + 6)

um:

x^{4} + 6 x^{3} - 7 x^{2} - 48 x - 36

x^{4} + 6 x^{3} - 7 x^{2} - 48 x - 36 = - 36

Verschiebe

36

auf die linke Seite

x^{4} + 6 x^{3} - 7 x^{2} - 48 x = 0

Faktorisiere

x^{4} + 6 x^{3} - 7 x^{2} - 48 x : x (x + 3) (x^{2} + 3 x - 16)

x (x + 3) (x^{2} + 3 x - 16) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x + 3 = 0 or x^{2} + 3 x - 16 = 0

Löse

x + 3 = 0 : x = - 3

Löse

x^{2} + 3 x - 16 = 0 : x = \frac{- 3 + 73}{2}, x = \frac{- 3 - 73}{2}

Die Lösungen sind

x = 0, x = - 3, x = \frac{- 3 + 73}{2}, x = \frac{- 3 - 73}{2}

Graph

Beliebte Beispiele

x+x^2-x^3-x^4=0

x + x^{2} - x^{3} - x^{4} = 0

4 x^{5} + 5 x^{2} - 3 x = 0

16 x^{4} + 8 x^{2} - 3 = 0

x^3-3x^2+3x-6=0

x^{3} - 3 x^{2} + 3 x - 6 = 0

x (x^{2} - 5 x + 14) = 0