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Beliebt Algebra >

30.7x^2+57=Ax(x+33.3)+B(x+33.3)+C*x^2

Lösung

30.7 \cdot x^{2} + 57 = A x (x + 33.3) + B \cdot (x + 33.3) + C \cdot x^{2}

Lösung

x = \frac{- 33.3 A - B + B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}, x = \frac{- 33.3 A - B - B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}; A + C - 30.7 \neq = 0

Schritte zur Lösung

30.7 x^{2} + 57 = A x (x + 33.3) + B (x + 33.3) + C x^{2}

Schreibe

A x (x + 33.3) + B (x + 33.3) + C x^{2}

um:

A x^{2} + 33.3 A x + B x + 33.3 B + C x^{2}

30.7 x^{2} + 57 = A x^{2} + 33.3 A x + B x + 33.3 B + C x^{2}

Tausche die Seiten

A x^{2} + 33.3 A x + B x + 33.3 B + C x^{2} = 30.7 x^{2} + 57

Verschiebe

57

auf die linke Seite

A x^{2} + 33.3 A x + B x + 33.3 B + C x^{2} - 57 = 30.7 x^{2}

Verschiebe

30.7 x^{2}

auf die linke Seite

A x^{2} + 33.3 A x + B x + 33.3 B + C x^{2} - 57 - 30.7 x^{2} = 0

Schreibe in der Standard Form

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

(A + C - 30.7) x^{2} + (33.3 A + B) x + 33.3 B - 57 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 33.3 A + B ) \pm ( 33.3 A + B ) ^{2} - 4 ( A + C - 30.7 ) ( 33.3 B - 57 )}{2 ( A + C - 30.7 )}

Vereinfache

(33.3 A + B)^{2} - 4 (A + C - 30.7) (33.3 B - 57) : B^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A^{2} + 228 A + 228 C - 6999.6

x_{1, 2} = \frac{- ( 33.3 A + B ) \pm B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}; A + C - 30.7 \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( 33.3 A + B ) + B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}, x_{2} = \frac{- ( 33.3 A + B ) - B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}

x = \frac{- ( 33.3 A + B ) + B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )} : \frac{- 33.3 A - B + B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}

x = \frac{- ( 33.3 A + B ) - B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )} : \frac{- 33.3 A - B - B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 33.3 A - B + B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}, x = \frac{- 33.3 A - B - B ^{2} - 66.6 A B - 133.2 BC + 4089.24 B + 1108.89 A ^{2} + 228 A + 228 C - 6999.6}{2 ( A + C - 30.7 )}; A + C - 30.7 \neq = 0

Graph

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