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Beliebt Algebra >

completesquare 2x^2+11x+15

Lösung

vervollständige das quadrat

2 x^{2} + 11 x + 15

Lösung

2 (x + \frac{11}{4})^{2} - \frac{1}{8}

Schritte zur Lösung

2 x^{2} + 11 x + 15

Schreibe

2 x^{2} + 11 x + 15

in dieser Form:

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

Klammere aus

2

2 (x^{2} + \frac{11 x}{2} + \frac{15}{2})

2 a = \frac{11}{2} : a = \frac{11}{4}

Addiere und subtrahiere

(\frac{11}{4})^{2}

2 (x^{2} + \frac{11 x}{2} + \frac{15}{2} + (\frac{11}{4})^{2} - (\frac{11}{4})^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

x^{2} + \frac{11}{2} x + (\frac{11}{4})^{2} = (x + \frac{11}{4})^{2}

2 ((x + \frac{11}{4})^{2} + \frac{15}{2} - (\frac{11}{4})^{2})

Vereinfache

2 (x + \frac{11}{4})^{2} - \frac{1}{8}

Graph

Beliebte Beispiele

x (2 x + 3) = 5

k^{2} = 49

- 1 = x^{2} - 2 x

1000=-16t^2+1700

1000 = - 16 t^{2} + 1700

x^{2} - 10 x - 119 = 0