completesquare x^2-1/3 x+1

Lösung

vervollständige das quadrat

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

(x - \frac{1}{6})^{2} + \frac{35}{36}

Schritte zur Lösung

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

Schreibe in der Standard Form

a x^{2} + b x + c

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

Schreibe

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

in dieser Form:

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

2 a = - \frac{1}{3} : a = - \frac{1}{6}

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

(x - \frac{1}{6})^{2} + \frac{35}{36}

(\frac{x - 7}{4})^{2} + (\frac{x - 3}{4})^{2} = \frac{169}{16}

4 x^{2} - 3 x = 7

0 = 6 x^{2} - 18 x + 12

3 x^{2} - 13 x = 0

5 x (x - 3) - x + 3 = 0