3x^2+2x+ax^2+5a+1=0

Lösung

3 x^{2} + 2 x + a x^{2} + 5 a + 1 = 0

x = \frac{- 1 + - 5 a ^{2} - 16 a - 2}{3 + a}, x = - \frac{- 5 a ^{2} - 16 a - 2 + 1}{a + 3}; a \neq = - 3

Schritte zur Lösung

3 x^{2} + 2 x + a x^{2} + 5 a + 1 = 0

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 ( 3 + a ) ( 5 a + 1 )}{2 ( 3 + a )}

Vereinfache

2^{2} - 4 (3 + a) (5 a + 1) : 2 - 5 a^{2} - 16 a - 2

x_{1, 2} = \frac{- 2 \pm 2 - 5 a ^{2} - 16 a - 2}{2 ( 3 + a )}; a \neq = - 3

Trenne die Lösungen

x_{1} = \frac{- 2 + 2 - 5 a ^{2} - 16 a - 2}{2 ( 3 + a )}, x_{2} = \frac{- 2 - 2 - 5 a ^{2} - 16 a - 2}{2 ( 3 + a )}

x = \frac{- 2 + 2 - 5 a ^{2} - 16 a - 2}{2 ( 3 + a )} : \frac{- 1 + - 5 a ^{2} - 16 a - 2}{3 + a}

x = \frac{- 2 - 2 - 5 a ^{2} - 16 a - 2}{2 ( 3 + a )} : - \frac{- 5 a ^{2} - 16 a - 2 + 1}{a + 3}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 1 + - 5 a ^{2} - 16 a - 2}{3 + a}, x = - \frac{- 5 a ^{2} - 16 a - 2 + 1}{a + 3}; a \neq = - 3

so l v e f or y, - 6 y^{2} - 21 = s (y^{2} + w)

co m pl e t es q u a re x^{2} - 6 x + 7

(x) = 2600 + 2 x + 0.001 x^{2}

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

4 x^{2} - 4 a^{2} x - b^{4} + a^{4} = 0