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Beliebt Algebra >

completesquare-3x^2-2x+12

Lösung

vervollständige das quadrat

- 3 x^{2} - 2 x + 12

Lösung

- 3 (x + \frac{1}{3})^{2} + \frac{37}{3}

Schritte zur Lösung

- 3 x^{2} - 2 x + 12

Schreibe

- 3 x^{2} - 2 x + 12

in dieser Form:

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

Klammere aus

- 3

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

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

Addiere und subtrahiere

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

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

Vereinfache

- 3 (x + \frac{1}{3})^{2} + \frac{37}{3}

Graph

Beliebte Beispiele

2 w^{2} + w - 7 = 0

3 x^{2} - 3 x - 10 = 0

4 x^{2} + 5 x + 5 = 0

(x - 3)^{2} + 5 = - 11

4 v^{2} - 9 v + 4 = 0