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

Lösung

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

x = \frac{- b ^{2} + b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}, x = \frac{- b ^{2} - b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}; a \neq = 0

Schritte zur Lösung

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

Löse mit der quadratischen Formel

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

Vereinfache

(b^{2})^{2} - 4 a^{2} c^{2} : b^{4} - 4 a^{2} c^{2}

x_{1, 2} = \frac{- b ^{2} \pm b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}; a \neq = 0

Trenne die Lösungen

x_{1} = \frac{- b ^{2} + b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}, x_{2} = \frac{- b ^{2} - b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}

x = \frac{- b ^{2} + b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}; a \neq = 0

x = \frac{- b ^{2} - b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}; a \neq = 0

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- b ^{2} + b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}, x = \frac{- b ^{2} - b ^{4} - 4 a ^{2} c ^{2}}{2 a ^{2}}; a \neq = 0

3 x (x + 6) = - 10

m^{2} + 2 m - 5 = 0

x^{2} + 2 x + 1 = x + 3

3 x^{2} - 5 = - 5 x - 3

6 a^{2} + 7 a - 11 = 5 a^{2}