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Beliebt Algebra >

completesquare 2x^2+x-6

Lösung

vervollständige das quadrat

2 x^{2} + x - 6

Lösung

2 (x + \frac{1}{4})^{2} - \frac{49}{8}

Schritte zur Lösung

2 x^{2} + x - 6

Schreibe

2 x^{2} + x - 6

in dieser Form:

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

Klammere aus

2

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

2 a = \frac{1}{2} : a = \frac{1}{4}

Addiere und subtrahiere

(\frac{1}{4})^{2}

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

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

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

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

Vereinfache

2 (x + \frac{1}{4})^{2} - \frac{49}{8}

Graph

Beliebte Beispiele

x^{2} - 5 = 0

4 x^{2} + 5 x + 10 = 2 x

x^{2} - 12 x + 39 = 0

(x + 11)^{2} = 64

(c - 1)^{2} + 7 = 3