(x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1

Lösung

(x - 1)^{2} + ((\frac{- 5}{12}) (\frac{x + 8}{5}))^{2} = + 1

x = \frac{8}{5}, x = \frac{8}{29}

Dezimale

x = 1.6, x = 0.27586 \dots

Schritte zur Lösung

(x - 1)^{2} + ((\frac{- 5}{12}) (\frac{x + 8}{5}))^{2} = 1

Schreibe

(x - 1)^{2} + ((\frac{- 5}{12}) (\frac{x + 8}{5}))^{2}

um:

\frac{145 x ^{2}}{144} - \frac{17 x}{9} + \frac{13}{9}

\frac{145 x ^{2}}{144} - \frac{17 x}{9} + \frac{13}{9} = 1

Verschiebe

1

auf die linke Seite

\frac{145 x ^{2}}{144} + \frac{- 17 x + 13}{9} - 1 = 0

Schreibe in der Standard Form

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

\frac{145 x ^{2}}{144} - \frac{17 x}{9} + \frac{13}{9} - 1 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - \frac{17}{9} ) \pm ( - \frac{17}{9} ) ^{2} - 4 \cdot \frac{145}{144} ( \frac{13}{9} - 1 )}{2 \cdot \frac{145}{144}}

(- \frac{17}{9})^{2} - 4 \cdot \frac{145}{144} (\frac{13}{9} - 1) = \frac{4}{3}

x_{1, 2} = \frac{- ( - \frac{17}{9} ) \pm \frac{4}{3}}{2 \cdot \frac{145}{144}}

Trenne die Lösungen

x_{1} = \frac{- ( - \frac{17}{9} ) + \frac{4}{3}}{2 \cdot \frac{145}{144}}, x_{2} = \frac{- ( - \frac{17}{9} ) - \frac{4}{3}}{2 \cdot \frac{145}{144}}

x = \frac{- ( - \frac{17}{9} ) + \frac{4}{3}}{2 \frac{145}{144}} : \frac{8}{5}

x = \frac{- ( - \frac{17}{9} ) - \frac{4}{3}}{2 \frac{145}{144}} : \frac{8}{29}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{8}{5}, x = \frac{8}{29}

x^{2} + 2 = 3 x

so l v e f or x, z = 4 - x^{2}

0 = x^{2} - 2 x - 15

x^{2} - 6 x + 17 = 0

4 x^{2} = - x - 1