3=(x-1)^2+(((-3)/4)*(x-1))^2

Lösung

3 = (x - 1)^{2} + ((\frac{- 3}{4}) \cdot (x - 1))^{2}

x = \frac{5 + 4 3}{5}, x = \frac{5 - 4 3}{5}

Dezimale

x = 2.38564 \dots, x = - 0.38564 \dots

Schritte zur Lösung

3 = (x - 1)^{2} + ((\frac{- 3}{4}) (x - 1))^{2}

Schreibe

(x - 1)^{2} + ((\frac{- 3}{4}) (x - 1))^{2}

um:

\frac{25}{16} x^{2} - \frac{25}{8} x + \frac{25}{16}

3 = \frac{25}{16} x^{2} - \frac{25}{8} x + \frac{25}{16}

Tausche die Seiten

\frac{25}{16} x^{2} - \frac{25}{8} x + \frac{25}{16} = 3

Verschiebe

3

auf die linke Seite

- \frac{23}{16} + \frac{25}{16} x^{2} - \frac{25}{8} x = 0

Schreibe in der Standard Form

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

\frac{25 x ^{2}}{16} - \frac{25 x}{8} - \frac{23}{16} = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - \frac{25}{8} ) \pm ( - \frac{25}{8} ) ^{2} - 4 \cdot \frac{25}{16} ( - \frac{23}{16} )}{2 \cdot \frac{25}{16}}

(- \frac{25}{8})^{2} - 4 \cdot \frac{25}{16} (- \frac{23}{16}) = \frac{5 3}{2}

x_{1, 2} = \frac{- ( - \frac{25}{8} ) \pm \frac{5 3}{2}}{2 \cdot \frac{25}{16}}

Trenne die Lösungen

x_{1} = \frac{- ( - \frac{25}{8} ) + \frac{5 3}{2}}{2 \cdot \frac{25}{16}}, x_{2} = \frac{- ( - \frac{25}{8} ) - \frac{5 3}{2}}{2 \cdot \frac{25}{16}}

x = \frac{- ( - \frac{25}{8} ) + \frac{5 3}{2}}{2 \frac{25}{16}} : \frac{5 + 4 3}{5}

x = \frac{- ( - \frac{25}{8} ) - \frac{5 3}{2}}{2 \frac{25}{16}} : \frac{5 - 4 3}{5}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{5 + 4 3}{5}, x = \frac{5 - 4 3}{5}

14 p^{2} + p - 6 = 2 p^{2}

- 63 x^{2} - 3 x + 6 = 0

(x + 9)^{2} + 8 (x + 9) + 7 = 0

- 45 = 0 + 10 t + \frac{1}{2} (- 9.8) t^{2}

4 (x - 7)^{2} + 25 = 69