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Beliebt Algebra >

completesquare 2x^2+6x+1

Lösung

vervollständige das quadrat

2 x^{2} + 6 x + 1

Lösung

2 (x + \frac{3}{2})^{2} - \frac{7}{2}

Schritte zur Lösung

2 x^{2} + 6 x + 1

Schreibe

2 x^{2} + 6 x + 1

in dieser Form:

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

Klammere aus

2

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

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

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

2 (x + \frac{3}{2})^{2} - \frac{7}{2}

Graph

Beliebte Beispiele

\frac{3}{2} x^{2} - 4 x - 1 = 0

x^{2} + 12 = 4 x

- 4 x^{2} - 2 x + 2 = 0

a x^{2} - a x + 8 = 0

x^{2} - 1 x - 3.75 = 0