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Beliebt Algebra >

completesquare 3x^2+2sqrt(3)x+15

Lösung

vervollständige das quadrat

3 x^{2} + 23 x + 15

Lösung

3 (x + \frac{1}{3})^{2} + 14

Schritte zur Lösung

3 x^{2} + 23 x + 15

Schreibe

3 x^{2} + 23 x + 15

in dieser Form:

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

Klammere aus

3

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

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

Addiere und subtrahiere

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

3 (x^{2} + \frac{2 x}{3} + 5 + (\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} + 5 - (\frac{1}{3})^{2})

Vereinfache

3 (x + \frac{1}{3})^{2} + 14

Graph

Beliebte Beispiele

4 - 3600 \cdot + x^{2} = 0

t^{2} - 22 t + 9 = 0

100x^2-10011x+10.011=0

100 x^{2} - 10011 x + 10.011 = 0

2 (x + 6)^{2} + 16 = 34

3 x^{2} + 168 = 36 x