2(a+5)x^2-(a+5)x+1=0

Lösung

2 (a + 5) \cdot x^{2} - (a + 5) \cdot x + 1 = 0

x = \frac{a + 5 + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}, x = \frac{a + 5 - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}; a \neq = - 5

Schritte zur Lösung

2 (a + 5) x^{2} - (a + 5) x + 1 = 0

Schreibe

2 (a + 5) x^{2} - (a + 5) x + 1

um:

2 a x^{2} + 10 x^{2} - a x - 5 x + 1

2 a x^{2} + 10 x^{2} - a x - 5 x + 1 = 0

Schreibe in der Standard Form

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

(2 a + 10) x^{2} - (a + 5) x + 1 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - a - 5 ) \pm ( - a - 5 ) ^{2} - 4 ( 2 a + 10 ) \cdot 1}{2 ( 2 a + 10 )}

Vereinfache

(- a - 5)^{2} - 4 (2 a + 10) \cdot 1 : a^{2} + 2 a - 15

x_{1, 2} = \frac{- ( - a - 5 ) \pm a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}; a \neq = - 5

Trenne die Lösungen

x_{1} = \frac{- ( - a - 5 ) + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}, x_{2} = \frac{- ( - a - 5 ) - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}

x = \frac{- ( - a - 5 ) + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )} : \frac{a + 5 + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}

x = \frac{- ( - a - 5 ) - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )} : \frac{a + 5 - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{a + 5 + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}, x = \frac{a + 5 - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}; a \neq = - 5

so l v e f or a, (1 + a + b)^{2} = 3 (a^{2} + b^{2} + 1)

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

so l v e f or x, \frac{x ^{2}}{( a ) ^{2}} + \frac{y ^{2}}{( b ) ^{2}} = 0

so l v e f or x, - (x - 1)^{2} + (y - 1)^{2} = 0

2 (y^{2} - 11) = 0