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}

x^{2} + 6^{2} = 9^{2}

2 x^{2} + 5 x = 5 x + 50

- 6 + 7 x + 3 x^{2} = 0

co m pl e t es q u a re 10 x^{2} - 3 x + 1

(2 x + 7)^{2} = 48