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Beliebt Algebra >

completesquare 3x^2+4x+5

Lösung

vervollständige das quadrat

3 x^{2} + 4 x + 5

Lösung

3 (x + \frac{2}{3})^{2} + \frac{11}{3}

Schritte zur Lösung

3 x^{2} + 4 x + 5

Schreibe

3 x^{2} + 4 x + 5

in dieser Form:

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

Klammere aus

3

3 (x^{2} + \frac{4 x}{3} + \frac{5}{3})

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

Addiere und subtrahiere

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

3 (x^{2} + \frac{4 x}{3} + \frac{5}{3} + (\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}

3 ((x + \frac{2}{3})^{2} + \frac{5}{3} - (\frac{2}{3})^{2})

Vereinfache

3 (x + \frac{2}{3})^{2} + \frac{11}{3}

Graph

Beliebte Beispiele

16 x^{2} - 34 = 15

f^{2} = 49

2 x^{2} + 12 x = 7

b^{2} + 16 b + 64 = 0

(- 3 - x)^{2} = 0