completesquare x^2-2/3 x+6

Lösung

vervollständige das quadrat

x^{2} - \frac{2}{3} x + 6

(x - \frac{1}{3})^{2} + \frac{53}{9}

Schritte zur Lösung

x^{2} - \frac{2}{3} x + 6

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} - \frac{2 x}{3} + 6

Schreibe

x^{2} - \frac{2 x}{3} + 6

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} + 6 + (- \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} + 6 - (- \frac{1}{3})^{2}

Vereinfache

(x - \frac{1}{3})^{2} + \frac{53}{9}

2 x^{2} + 11 x - 3 = 0

2 x^{2} = 1 + x^{2}

0 = x^{2} - x + 1

7500000 = - 0.5 x^{2} + 2000 x + 6000000

3 x^{2} + 30 x + 75 = 0