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Beliebt Algebra >

completesquare 4x^2+4x+1

Lösung

vervollständige das quadrat

4 x^{2} + 4 x + 1

Lösung

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

Schritte zur Lösung

4 x^{2} + 4 x + 1

Schreibe

4 x^{2} + 4 x + 1

in dieser Form:

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

Klammere aus

4

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

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

Addiere und subtrahiere

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

x^{2} + 22 x + 4 = 0

3 x^{2} - 6 x - 23 = 0

6 x = 2 x^{2} + 1

x^{2} - 2 x + a^{2} - 1 = 0

- 2 x^{2} + 4 x - 3 = 0