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Beliebt Algebra >

completesquare 2x^2+3x-2

Lösung

vervollständige das quadrat

2 x^{2} + 3 x - 2

Lösung

2 (x + \frac{3}{4})^{2} - \frac{25}{8}

Schritte zur Lösung

2 x^{2} + 3 x - 2

Schreibe

2 x^{2} + 3 x - 2

in dieser Form:

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

Klammere aus

2

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

2 a = \frac{3}{2} : a = \frac{3}{4}

Addiere und subtrahiere

(\frac{3}{4})^{2}

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

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

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

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

Vereinfache

2 (x + \frac{3}{4})^{2} - \frac{25}{8}

Graph

Beliebte Beispiele

x^{2} + 6 = 7 x

3 x^{2} + 300 = 0

x^{2} + 5 x = 3

7 x^{2} = 5 x + 7

5 x^{2} + 21 x + 4 = 0