a^{0.2}x(7x+5)-7x(2x-3)=93

Lösung

a^{0.2} x (7 x + 5) - 7 x (2 x - 3) = 93

x = \frac{- 5 a ^{0.2} - 21 + 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}, x = \frac{- 5 a ^{0.2} - 21 - 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}; a \neq = 32

Schritte zur Lösung

a^{0.2} x (7 x + 5) - 7 x (2 x - 3) = 93

Schreibe

a^{0.2} x (7 x + 5) - 7 x (2 x - 3)

um:

7 a^{0.2} x^{2} + 5 a^{0.2} x - 14 x^{2} + 21 x

7 a^{0.2} x^{2} + 5 a^{0.2} x - 14 x^{2} + 21 x = 93

Verschiebe

93

auf die linke Seite

7 a^{0.2} x^{2} + 5 a^{0.2} x - 14 x^{2} + 21 x - 93 = 0

Schreibe in der Standard Form

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

(7 a^{0.2} - 14) x^{2} + (5 a^{0.2} + 21) x - 93 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 5 a ^{0.2} + 21 ) \pm ( 5 a ^{0.2} + 21 ) ^{2} - 4 ( 7 a ^{0.2} - 14 ) ( - 93 )}{2 ( 7 a ^{0.2} - 14 )}

Vereinfache

(5 a^{0.2} + 21)^{2} - 4 (7 a^{0.2} - 14) (- 93) : 25 a^{0.4} + 2814 a^{0.2} - 4767

x_{1, 2} = \frac{- ( 5 a ^{0.2} + 21 ) \pm 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}; a \neq = 32

Trenne die Lösungen

x_{1} = \frac{- ( 5 a ^{0.2} + 21 ) + 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}, x_{2} = \frac{- ( 5 a ^{0.2} + 21 ) - 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}

x = \frac{- ( 5 a ^{0.2} + 21 ) + 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )} : \frac{- 5 a ^{0.2} - 21 + 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}

x = \frac{- ( 5 a ^{0.2} + 21 ) - 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )} : \frac{- 5 a ^{0.2} - 21 - 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 5 a ^{0.2} - 21 + 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}, x = \frac{- 5 a ^{0.2} - 21 - 25 a ^{0.4} + 2814 a ^{0.2} - 4767}{2 ( 7 a ^{0.2} - 14 )}; a \neq = 32

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