0.75(0.25-x+x^2)=x^2

Lösung

0.75 (0.25 - x + x^{2}) = x^{2}

x = - \frac{0.75 + 0.75}{0.5}, x = \frac{0.75 - 0.75}{0.5}

Dezimale

x = - 3.23205 \dots, x = 0.23205 \dots

Schritte zur Lösung

0.75 (0.25 - x + x^{2}) = x^{2}

Schreibe

0.75 (0.25 - x + x^{2})

um:

0.1875 - 0.75 x + 0.75 x^{2}

0.1875 - 0.75 x + 0.75 x^{2} = x^{2}

Verschiebe

x^{2}

auf die linke Seite

0.1875 - 0.75 x - 0.25 x^{2} = 0

Schreibe in der Standard Form

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

- 0.25 x^{2} - 0.75 x + 0.1875 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 0.75 ) \pm ( - 0.75 ) ^{2} - 4 ( - 0.25 ) \cdot 0.1875}{2 ( - 0.25 )}

(- 0.75)^{2} - 4 (- 0.25) \cdot 0.1875 = 0.75

x_{1, 2} = \frac{- ( - 0.75 ) \pm 0.75}{2 ( - 0.25 )}

Trenne die Lösungen

x_{1} = \frac{- ( - 0.75 ) + 0.75}{2 ( - 0.25 )}, x_{2} = \frac{- ( - 0.75 ) - 0.75}{2 ( - 0.25 )}

x = \frac{- ( - 0.75 ) + 0.75}{2 ( - 0.25 )} : - \frac{0.75 + 0.75}{0.5}

x = \frac{- ( - 0.75 ) - 0.75}{2 ( - 0.25 )} : \frac{0.75 - 0.75}{0.5}

Die Lösungen für die quadratische Gleichung sind:

x = - \frac{0.75 + 0.75}{0.5}, x = \frac{0.75 - 0.75}{0.5}

a = 3 x^{2} - 9 x

so l v e f or x, z = x^{2} - 8 x y + 5 y + 7

a = 3 r^{2}

so l v e f or x, x^{2} + 3 x + 1 = 5^{y}

so l v e f or x, x^{2} + y^{2} + z^{3} = 6