solvefor x,F=(m-2)x^2+(n-1)x+(p-3)

Lösung

löse nach

x, F = (m - 2) x^{2} + (n - 1) x + (p - 3)

x = \frac{- n + 1 + 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}, x = \frac{- n + 1 - 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}; m \neq = 2

Schritte zur Lösung

F = (m - 2) x^{2} + (n - 1) x + (p - 3)

Schreibe

(m - 2) x^{2} + (n - 1) x + (p - 3)

um:

m x^{2} - 2 x^{2} + n x - x + p - 3

F = m x^{2} - 2 x^{2} + n x - x + p - 3

Tausche die Seiten

m x^{2} - 2 x^{2} + n x - x + p - 3 = F

Verschiebe

F

auf die linke Seite

m x^{2} - 2 x^{2} + n x - x + p - 3 - F = 0

Schreibe in der Standard Form

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

(m - 2) x^{2} + (n - 1) x + p - 3 - F = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( n - 1 ) \pm ( n - 1 ) ^{2} - 4 ( m - 2 ) ( p - 3 - F )}{2 ( m - 2 )}

Vereinfache

(n - 1)^{2} - 4 (m - 2) (p - 3 - F) : 4 m F - 8 F + 12 m + n^{2} + 8 p - 4 m p - 2 n - 23

x_{1, 2} = \frac{- ( n - 1 ) \pm 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}; m \neq = 2

Trenne die Lösungen

x_{1} = \frac{- ( n - 1 ) + 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}, x_{2} = \frac{- ( n - 1 ) - 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}

x = \frac{- ( n - 1 ) + 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )} : \frac{- n + 1 + 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}

x = \frac{- ( n - 1 ) - 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )} : \frac{- n + 1 - 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- n + 1 + 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}, x = \frac{- n + 1 - 4 m F - 8 F + 12 m + n ^{2} + 8 p - 4 m p - 2 n - 23}{2 ( m - 2 )}; m \neq = 2

(x + 9)^{2} = 12

so l v e f or x, x^{2} + 4 x - 2 a y + 2 (2 - a^{2}) = 0

7 x^{2} = 23 x

f a c t or 4 x^{2} + 16 x = 0

x^{2} + \frac{x}{2} - \frac{1}{2} = 0