completesquare 6x^2+8x+9

Lösung

vervollständige das quadrat

6 x^{2} + 8 x + 9

6 (x + \frac{2}{3})^{2} + \frac{19}{3}

Schritte zur Lösung

6 x^{2} + 8 x + 9

Schreibe

6 x^{2} + 8 x + 9

in dieser Form:

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

Klammere aus

6

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

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

Addiere und subtrahiere

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

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

Vereinfache

6 (x + \frac{2}{3})^{2} + \frac{19}{3}

roo t s s^{2} + 2 s + 5

5 x^{2} - 2 = - 92

co m pl e t es q u a re 2 x^{2} + 12 x + 4

6 + 3 x^{2} = 18

roo t s x^{2} + 16