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Beliebt Algebra >

completesquare 2x^2-2x-3

Lösung

vervollständige das quadrat

2 x^{2} - 2 x - 3

Lösung

2 (x - \frac{1}{2})^{2} - \frac{7}{2}

Schritte zur Lösung

2 x^{2} - 2 x - 3

Schreibe

2 x^{2} - 2 x - 3

in dieser Form:

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

Klammere aus

2

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

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

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

2 (x - \frac{1}{2})^{2} - \frac{7}{2}

Graph

Beliebte Beispiele

8 x (x - 6) = 0

- 5 x^{2} + 6 x - 5 = 0

- 3 x^{2} + 10 x - 8 = 0

0.005=2(0.005)(1-(r/(0.005))^2)

0.005 = 2 (0.005) (1 - (\frac{r}{0.005})^{2})

5 x (x - 6) = x - 30