completesquare x^2-2/3 x

Lösung

vervollständige das quadrat

x^{2} - \frac{2}{3} x

(x - \frac{1}{3})^{2} - \frac{1}{9}

Schritte zur Lösung

x^{2} - \frac{2}{3} x

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} - \frac{2 x}{3}

Schreibe

x^{2} - \frac{2 x}{3}

in dieser Form:

x^{2} + 2 a x + a^{2}

2 a = - \frac{2}{3} : a = - \frac{1}{3}

Addiere und subtrahiere

(- \frac{1}{3})^{2}

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

x^{2} + 2 a x + a^{2} = (x + a)^{2}

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

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

Vereinfache

(x - \frac{1}{3})^{2} - \frac{1}{9}

(x + 5)^{2} + 16 = 0

(x + 2) (x - 1) = 10

0 = 4 x^{2} - 4 x + 1

\frac{x ^{2}}{5} - \frac{x}{2} = \frac{4}{5}

y^{2} + 1 = \frac{y + 8}{2}