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Beliebt Algebra >

x^2+x-a(a+1)=0

Lösung

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

Lösung

x = a, x = - a - 1

Schritte zur Lösung

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

Schreibe

x^{2} + x - a (a + 1)

um:

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

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

Faktorisiere

x^{2} + x - a^{2} - a : (x - a) (x + a + 1)

(x - a) (x + a + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - a = 0 or x + a + 1 = 0

Löse

x - a = 0 : x = a

Löse

x + a + 1 = 0 : x = - a - 1

Die Lösungen für die quadratische Gleichung sind:

x = a, x = - a - 1

Graph

Beliebte Beispiele

solvefor x,(x-1)^2+(y-1)^2=((x-y-3)^2)/2

so l v e f or x, (x - 1)^{2} + (y - 1)^{2} = \frac{( x - y - 3 ) ^{2}}{2}

(x^2+x)/((sqrt(2))+1)=0

\frac{x ^{2} + x}{( 2 ) + 1} = 0

(d^{3} - 3 d - 2) = x^{2}

14x^1-3x^2=8,x^1+5x^2=11

14 x^{1} - 3 x^{2} = 8, x^{1} + 5 x^{2} = 11

solvefor y,y^2=x(x^2-3)

so l v e f or y, y^{2} = x (x^{2} - 3)