8x^2-(k-1)x+(k-7)=0

Lösung

8 x^{2} - (k - 1) x + (k - 7) = 0

x = \frac{k - 1 + k ^{2} - 34 k + 225}{16}, x = \frac{k - 1 - k ^{2} - 34 k + 225}{16}

Schritte zur Lösung

8 x^{2} - (k - 1) x + (k - 7) = 0

Schreibe

8 x^{2} - (k - 1) x + (k - 7)

um:

8 x^{2} - k x + x + k - 7

8 x^{2} - k x + x + k - 7 = 0

Schreibe in der Standard Form

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

8 x^{2} + (- k + 1) x + k - 7 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - k + 1 ) \pm ( - k + 1 ) ^{2} - 4 \cdot 8 ( k - 7 )}{2 \cdot 8}

Vereinfache

(- k + 1)^{2} - 4 \cdot 8 (k - 7) : k^{2} - 34 k + 225

x_{1, 2} = \frac{- ( - k + 1 ) \pm k ^{2} - 34 k + 225}{2 \cdot 8}

Trenne die Lösungen

x_{1} = \frac{- ( - k + 1 ) + k ^{2} - 34 k + 225}{2 \cdot 8}, x_{2} = \frac{- ( - k + 1 ) - k ^{2} - 34 k + 225}{2 \cdot 8}

x = \frac{- ( - k + 1 ) + k ^{2} - 34 k + 225}{2 \cdot 8} : \frac{k - 1 + k ^{2} - 34 k + 225}{16}

x = \frac{- ( - k + 1 ) - k ^{2} - 34 k + 225}{2 \cdot 8} : \frac{k - 1 - k ^{2} - 34 k + 225}{16}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{k - 1 + k ^{2} - 34 k + 225}{16}, x = \frac{k - 1 - k ^{2} - 34 k + 225}{16}

so l v e f or F = G \frac{mm}{r ^{2}}, m

3 x^{2} - 13 = 35

a^{2} - 11 a = 0

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

(k - 4)^{2} = 169