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Beliebt Algebra >

completesquare 4x^2+12x+9

Lösung

vervollständige das quadrat

4 x^{2} + 12 x + 9

Lösung

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

Schritte zur Lösung

4 x^{2} + 12 x + 9

Schreibe

4 x^{2} + 12 x + 9

in dieser Form:

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

Klammere aus

4

4 (x^{2} + 3 x + \frac{9}{4})

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

Addiere und subtrahiere

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

4 (x^{2} + 3 x + \frac{9}{4} + (\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}

4 ((x + \frac{3}{2})^{2} + \frac{9}{4} - (\frac{3}{2})^{2})

Vereinfache

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

Graph

Beliebte Beispiele

- 3 x^{2} + 5 x - 3 = 0

4 x^{2} - 5 x = 6

(x + 2) (x - 7) = 0

x^{2} - 8 x - 240 = 0

(x+2)(x-5)=6-3x

(x + 2) (x - 5) = 6 - 3 x