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Beliebt Algebra >

(81x^2-100)(x^2-14)=0

Lösung

(81 x^{2} - 100) (x^{2} - 14) = 0

Lösung

x = - \frac{10}{9}, x = \frac{10}{9}, x = - 14, x = 14

+1

Dezimale

x = - 1.11111 \dots, x = 1.11111 \dots, x = - 3.74165 \dots, x = 3.74165 \dots

Schritte zur Lösung

(81 x^{2} - 100) (x^{2} - 14) = 0

Faktorisiere

(81 x^{2} - 100) (x^{2} - 14) : (9 x + 10) (9 x - 10) (x + 14) (x - 14)

(9 x + 10) (9 x - 10) (x + 14) (x - 14) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

9 x + 10 = 0 or 9 x - 10 = 0 or x + 14 = 0 or x - 14 = 0

Löse

9 x + 10 = 0 : x = - \frac{10}{9}

Löse

9 x - 10 = 0 : x = \frac{10}{9}

Löse

x + 14 = 0 : x = - 14

Löse

x - 14 = 0 : x = 14

Die Lösungen sind

x = - \frac{10}{9}, x = \frac{10}{9}, x = - 14, x = 14

Graph

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