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Beliebt Algebra >

4(x+4)^4-53(x+4)^2=-49

Lösung

4 (x + 4)^{4} - 53 (x + 4)^{2} = - 49

Lösung

x = - 3, x = - 5, x = - \frac{1}{2}, x = - \frac{15}{2}

+1

Dezimale

x = - 3, x = - 5, x = - 0.5, x = - 7.5

Schritte zur Lösung

4 (x + 4)^{4} - 53 (x + 4)^{2} = - 49

Schreibe

4 (x + 4)^{4} - 53 (x + 4)^{2}

um:

4 x^{4} + 64 x^{3} + 331 x^{2} + 600 x + 176

4 x^{4} + 64 x^{3} + 331 x^{2} + 600 x + 176 = - 49

Verschiebe

49

auf die linke Seite

4 x^{4} + 64 x^{3} + 331 x^{2} + 600 x + 225 = 0

Faktorisiere

4 x^{4} + 64 x^{3} + 331 x^{2} + 600 x + 225 : (x + 3) (x + 5) (2 x + 1) (2 x + 15)

(x + 3) (x + 5) (2 x + 1) (2 x + 15) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 3 = 0 or x + 5 = 0 or 2 x + 1 = 0 or 2 x + 15 = 0

Löse

x + 3 = 0 : x = - 3

Löse

x + 5 = 0 : x = - 5

Löse

2 x + 1 = 0 : x = - \frac{1}{2}

Löse

2 x + 15 = 0 : x = - \frac{15}{2}

Die Lösungen sind

x = - 3, x = - 5, x = - \frac{1}{2}, x = - \frac{15}{2}

Graph

Beliebte Beispiele

0=x^3-2x^2-11x+12

0 = x^{3} - 2 x^{2} - 11 x + 12

a \cdot a \cdot a = 3 a

2x^3+3x^2-17x+12=0

2 x^{3} + 3 x^{2} - 17 x + 12 = 0

z^{4} - 49 = 0

0.000004x^3-400=0

0.000004 x^{3} - 400 = 0