completesquare 9x^2-6x-3

Lösung

vervollständige das quadrat

9 x^{2} - 6 x - 3

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

Schritte zur Lösung

9 x^{2} - 6 x - 3

Schreibe

9 x^{2} - 6 x - 3

in dieser Form:

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

Klammere aus

9

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

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

Addiere und subtrahiere

(- \frac{1}{3})^{2}

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

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

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

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

Vereinfache

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

(x - 4) (x + 2) = 5

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

c = 3100 - c^{2}

- 4.9 x^{2} + 10 x + 20 = 0

co m pl e t es q u a re 5 x^{2} + 3 x - 4