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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

(2 x + 3)^{2} = 9

(x - 1) (2 x + 5) = 0

6x(x-2)-3=2(x-2)(x+2)-4

6 x (x - 2) - 3 = 2 (x - 2) (x + 2) - 4

7-0.0000003x^2+0.0006x-6=0

7 - 0.0000003 x^{2} + 0.0006 x - 6 = 0

3 u^{2} = 24 u - 3