completesquare 3x^2-5x+1

Lösung

vervollständige das quadrat

3 x^{2} - 5 x + 1

3 (x - \frac{5}{6})^{2} - \frac{13}{12}

Schritte zur Lösung

3 x^{2} - 5 x + 1

Schreibe

3 x^{2} - 5 x + 1

in dieser Form:

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

Klammere aus

3

3 (x^{2} - \frac{5 x}{3} + \frac{1}{3})

2 a = - \frac{5}{3} : a = - \frac{5}{6}

Addiere und subtrahiere

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

3 (x^{2} - \frac{5 x}{3} + \frac{1}{3} + (- \frac{5}{6})^{2} - (- \frac{5}{6})^{2})

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

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

3 ((x - \frac{5}{6})^{2} + \frac{1}{3} - (- \frac{5}{6})^{2})

Vereinfache

3 (x - \frac{5}{6})^{2} - \frac{13}{12}

(6 x - 3) (2 x + 4) = 3

4 x^{2} - 2 x + 10 = 0

x^{2} + 9 x = 27

co m pl e t es q u a re 2 x^{2} - 10 x + 9 = 0

100 x^{2} = 1