completesquare 6x^2-8x+1

Lösung

vervollständige das quadrat

6 x^{2} - 8 x + 1

6 (x - \frac{2}{3})^{2} - \frac{5}{3}

Schritte zur Lösung

6 x^{2} - 8 x + 1

Schreibe

6 x^{2} - 8 x + 1

in dieser Form:

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

Klammere aus

6

6 (x^{2} - \frac{4 x}{3} + \frac{1}{6})

2 a = - \frac{4}{3} : a = - \frac{2}{3}

Addiere und subtrahiere

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

6 (x^{2} - \frac{4 x}{3} + \frac{1}{6} + (- \frac{2}{3})^{2} - (- \frac{2}{3})^{2})

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

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

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

Vereinfache

6 (x - \frac{2}{3})^{2} - \frac{5}{3}

(r - 7)^{2} = 81

2 x^{2} - 7 x + 9 = (x - 3) (x + 1) + 3 x

2 x (x + 3) + 1 = 0

(x + 2)^{3} = x (x^{2} - 10 x + 25)

5 x^{2} + 20 x + 19 = 0