4.5x^2=2.5(x+0.5)^2

Lösung

4.5 x^{2} = 2.5 (x + 0.5)^{2}

x = - \frac{- 2.5 + 11.25}{4}, x = \frac{2.5 + 11.25}{4}

Dezimale

x = - 0.21352 \dots, x = 1.46352 \dots

Schritte zur Lösung

4.5 x^{2} = 2.5 (x + 0.5)^{2}

Schreibe

2.5 (x + 0.5)^{2}

um:

2.5 x^{2} + 2.5 x + 0.625

4.5 x^{2} = 2.5 x^{2} + 2.5 x + 0.625

Tausche die Seiten

2.5 x^{2} + 2.5 x + 0.625 = 4.5 x^{2}

Verschiebe

4.5 x^{2}

auf die linke Seite

- 2 x^{2} + 2.5 x + 0.625 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- 2.5 \pm 2. 5 ^{2} - 4 ( - 2 ) \cdot 0.625}{2 ( - 2 )}

2. 5^{2} - 4 (- 2) \cdot 0.625 = 11.25

x_{1, 2} = \frac{- 2.5 \pm 11.25}{2 ( - 2 )}

Trenne die Lösungen

x_{1} = \frac{- 2.5 + 11.25}{2 ( - 2 )}, x_{2} = \frac{- 2.5 - 11.25}{2 ( - 2 )}

x = \frac{- 2.5 + 11.25}{2 ( - 2 )} : - \frac{- 2.5 + 11.25}{4}

x = \frac{- 2.5 - 11.25}{2 ( - 2 )} : \frac{2.5 + 11.25}{4}

Die Lösungen für die quadratische Gleichung sind:

x = - \frac{- 2.5 + 11.25}{4}, x = \frac{2.5 + 11.25}{4}

x^{2} + 27 = 12 x

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

so l v e f or x, (x - 5) (3 x + 2) = 0

4 x^{2} - 2 x - 11 = 0

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