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Beliebt Algebra >

completesquare 2x^2+9x+4

Lösung

vervollständige das quadrat

2 x^{2} + 9 x + 4

Lösung

2 (x + \frac{9}{4})^{2} - \frac{49}{8}

Schritte zur Lösung

2 x^{2} + 9 x + 4

Schreibe

2 x^{2} + 9 x + 4

in dieser Form:

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

Klammere aus

2

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

2 a = \frac{9}{2} : a = \frac{9}{4}

Addiere und subtrahiere

(\frac{9}{4})^{2}

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

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

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

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

Vereinfache

2 (x + \frac{9}{4})^{2} - \frac{49}{8}

Graph

Beliebte Beispiele

8x^2-2(x+10)=10x

8 x^{2} - 2 (x + 10) = 10 x

(2 x + 1) (x - 2) = 5

solvefor x,x^2+y^2+18=0

so l v e f or x, x^{2} + y^{2} + 18 = 0

8 = 3 x^{2} - 2 x

2 x (x + 2) = 0