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Beliebt Algebra >

completesquare x^2+1/2 x+2

Lösung

vervollständige das quadrat

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

Lösung

(x + \frac{1}{4})^{2} + \frac{31}{16}

Schritte zur Lösung

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

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} + \frac{x}{2} + 2

Schreibe

x^{2} + \frac{x}{2} + 2

in dieser Form:

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

2 a = \frac{1}{2} : a = \frac{1}{4}

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

(x + \frac{1}{4})^{2} + \frac{31}{16}

Graph

Beliebte Beispiele

6 x^{2} + 1 = - 5

s^{2} + 5 s + 2 = 0

(x^{2} + 2 x + 3) = 0

- x^{2} + 10 x = 21

w^{2} + 5 w - 4 = 0