2ax^2+(2a^2-a-4)x-(2+a^2)=0

Lösung

2 a x^{2} + (2 a^{2} - a - 4) x - (2 + a^{2}) = 0

x = \frac{- 2 a ^{2} + a + 4 + 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{4 a}, x = \frac{- 2 a ^{2} + a + 4 - 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{4 a}; a \neq = 0

Schritte zur Lösung

2 a x^{2} + (2 a^{2} - a - 4) x - (2 + a^{2}) = 0

Schreibe

2 a x^{2} + (2 a^{2} - a - 4) x - (2 + a^{2})

um:

2 a x^{2} + 2 a^{2} x - a x - 4 x - 2 - a^{2}

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

Schreibe in der Standard Form

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

2 a x^{2} + (2 a^{2} - a - 4) x - 2 - a^{2} = 0

Löse mit der quadratischen Formel

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

Vereinfache

(2 a^{2} - a - 4)^{2} - 4 \cdot 2 a (- 2 - a^{2}) : 4 a^{4} + 4 a^{3} - 15 a^{2} + 24 a + 16

x_{1, 2} = \frac{- ( 2 a ^{2} - a - 4 ) \pm 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{2 \cdot 2 a}; a \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( 2 a ^{2} - a - 4 ) + 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{2 \cdot 2 a}, x_{2} = \frac{- ( 2 a ^{2} - a - 4 ) - 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{2 \cdot 2 a}

x = \frac{- ( 2 a ^{2} - a - 4 ) + 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{2 \cdot 2 a} : \frac{- 2 a ^{2} + a + 4 + 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{4 a}

x = \frac{- ( 2 a ^{2} - a - 4 ) - 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{2 \cdot 2 a} : \frac{- 2 a ^{2} + a + 4 - 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{4 a}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 2 a ^{2} + a + 4 + 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{4 a}, x = \frac{- 2 a ^{2} + a + 4 - 4 a ^{4} + 4 a ^{3} - 15 a ^{2} + 24 a + 16}{4 a}; a \neq = 0

(x + 8)^{2} - 1 = 0

\frac{( x ^{2} + 4 x )}{4} = 24

n^{2} + 8 n + 12 = 0

(x - 3) (x + 4) = 6

10 x^{2} + 9 = 509