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Beliebt Algebra >

completesquare 2x^2+5x+2

Lösung

vervollständige das quadrat

2 x^{2} + 5 x + 2

Lösung

2 (x + \frac{5}{4})^{2} - \frac{9}{8}

Schritte zur Lösung

2 x^{2} + 5 x + 2

Schreibe

2 x^{2} + 5 x + 2

in dieser Form:

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

Klammere aus

2

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

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

Addiere und subtrahiere

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

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

Vereinfache

2 (x + \frac{5}{4})^{2} - \frac{9}{8}

Graph

Beliebte Beispiele

solvefor x,xy+2x+3x^2=4

so l v e f or x, x y + 2 x + 3 x^{2} = 4

4/3 x^2= 2/3 x^2+6

\frac{4}{3} x^{2} = \frac{2}{3} x^{2} + 6

completesquare x^2-2x-4

co m pl e t es q u a re x^{2} - 2 x - 4

completesquare x^2-2x-2

co m pl e t es q u a re x^{2} - 2 x - 2

completesquare x^2-2x+3

co m pl e t es q u a re x^{2} - 2 x + 3