0.534(0.5-x)^2=x^2

Lösung

0.534 (0.5 - x)^{2} = x^{2}

x = - \frac{0.534 + 0.534}{0.932}, x = \frac{0.534 - 0.534}{0.932}

Dezimale

x = - 1.35703 \dots, x = 0.21110 \dots

Schritte zur Lösung

0.534 (0.5 - x)^{2} = x^{2}

Schreibe

0.534 (0.5 - x)^{2}

um:

0.1335 - 0.534 x + 0.534 x^{2}

0.1335 - 0.534 x + 0.534 x^{2} = x^{2}

Verschiebe

x^{2}

auf die linke Seite

0.1335 - 0.534 x - 0.466 x^{2} = 0

Schreibe in der Standard Form

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

- 0.466 x^{2} - 0.534 x + 0.1335 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 0.534 ) \pm ( - 0.534 ) ^{2} - 4 ( - 0.466 ) \cdot 0.1335}{2 ( - 0.466 )}

(- 0.534)^{2} - 4 (- 0.466) \cdot 0.1335 = 0.534

x_{1, 2} = \frac{- ( - 0.534 ) \pm 0.534}{2 ( - 0.466 )}

Trenne die Lösungen

x_{1} = \frac{- ( - 0.534 ) + 0.534}{2 ( - 0.466 )}, x_{2} = \frac{- ( - 0.534 ) - 0.534}{2 ( - 0.466 )}

x = \frac{- ( - 0.534 ) + 0.534}{2 ( - 0.466 )} : - \frac{0.534 + 0.534}{0.932}

x = \frac{- ( - 0.534 ) - 0.534}{2 ( - 0.466 )} : \frac{0.534 - 0.534}{0.932}

Die Lösungen für die quadratische Gleichung sind:

x = - \frac{0.534 + 0.534}{0.932}, x = \frac{0.534 - 0.534}{0.932}

so l v e f or x, f (x^{2}) = 3 (x^{2}) + 2

3 x^{2} - 7 = 7 x - 1

x^{2} - 3 = 2 x + 5

5 x^{2} + 10 x - 40 = 0

x^{2} + 6 x - 2 = 7 x + 10