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Beliebt Algebra >

completesquare 2x^2+5x-1

Lösung

vervollständige das quadrat

2 x^{2} + 5 x - 1

Lösung

2 (x + \frac{5}{4})^{2} - \frac{33}{8}

Schritte zur Lösung

2 x^{2} + 5 x - 1

Schreibe

2 x^{2} + 5 x - 1

in dieser Form:

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

Klammere aus

2

2 (x^{2} + \frac{5 x}{2} - \frac{1}{2})

2 a = \frac{5}{2} : a = \frac{5}{4}

Addiere und subtrahiere

(\frac{5}{4})^{2}

2 (x^{2} + \frac{5 x}{2} - \frac{1}{2} + (\frac{5}{4})^{2} - (\frac{5}{4})^{2})

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

x^{2} + \frac{5}{2} x + (\frac{5}{4})^{2} = (x + \frac{5}{4})^{2}

2 ((x + \frac{5}{4})^{2} - \frac{1}{2} - (\frac{5}{4})^{2})

Vereinfache

2 (x + \frac{5}{4})^{2} - \frac{33}{8}

Graph

Beliebte Beispiele

completesquare 2x^2+5x+1

co m pl e t es q u a re 2 x^{2} + 5 x + 1

9 y^{2} - y + 7 = 0

(x - 121)^{2} = 0

(x - 7)^{2} = 121

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