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

Lösung

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

x = \frac{a + 2 + a ^{2} - 16}{2 ( a + 5 )}, x = \frac{a + 2 - a ^{2} - 16}{2 ( a + 5 )}; a \neq = - 5

Schritte zur Lösung

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

Verschiebe

(a + 2) x

auf die linke Seite

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

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

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

Vereinfache

(- a - 2)^{2} - 4 (a + 5) \cdot 1 : a^{2} - 16

x_{1, 2} = \frac{- ( - a - 2 ) \pm a ^{2} - 16}{2 ( a + 5 )}; a \neq = - 5

Trenne die Lösungen

x_{1} = \frac{- ( - a - 2 ) + a ^{2} - 16}{2 ( a + 5 )}, x_{2} = \frac{- ( - a - 2 ) - a ^{2} - 16}{2 ( a + 5 )}

x = \frac{- ( - a - 2 ) + a ^{2} - 16}{2 ( a + 5 )} : \frac{a + 2 + a ^{2} - 16}{2 ( a + 5 )}

x = \frac{- ( - a - 2 ) - a ^{2} - 16}{2 ( a + 5 )} : \frac{a + 2 - a ^{2} - 16}{2 ( a + 5 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{a + 2 + a ^{2} - 16}{2 ( a + 5 )}, x = \frac{a + 2 - a ^{2} - 16}{2 ( a + 5 )}; a \neq = - 5

x^{2} - 84 = 2 x - 4

so l v e f or y, 2 x^{2} + x y + y^{2} = 4

2 w^{2} + 9 w - 10 = 6 w

3 x^{2} + 7 x + 10 = 0

co m pl e t es q u a re x^{2} - 2 x - 3