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Beliebt Algebra >

completesquare 3x^2+2x-1

Lösung

vervollständige das quadrat

3 x^{2} + 2 x - 1

Lösung

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}

Graph

Beliebte Beispiele

x^{2} + b x + c = 0

3 x^{2} + 5 = 5 x^{2} - 8 x

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x^{2} + 64 = - 20 x

x^{2} - 2.5 x + 1.5 = 0