completesquare-3x^2+2x+1

Lösung

vervollständige das quadrat

- 3 x^{2} + 2 x + 1

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

Schritte zur Lösung

- 3 x^{2} + 2 x + 1

Schreibe

- 3 x^{2} + 2 x + 1

in dieser Form:

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

Klammere aus

- 3

- 3 (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}

- 3 (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}

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

Vereinfache

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

4.9 x^{2} - 10 x = 0

so l v e f or U, A = 18 X^{2} - 27 X U^{2}

q^{2} = - 5

\frac{1}{4} (x + 3)^{2} + 6 = 0

2 y^{2} - 7 y = 7