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Beliebt Algebra >

completesquare x^2+1/3 x+3

Lösung

vervollständige das quadrat

x^{2} + \frac{1}{3} x + 3

Lösung

(x + \frac{1}{6})^{2} + \frac{107}{36}

Schritte zur Lösung

x^{2} + \frac{1}{3} x + 3

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} + \frac{x}{3} + 3

Schreibe

x^{2} + \frac{x}{3} + 3

in dieser Form:

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

2 a = \frac{1}{3} : a = \frac{1}{6}

Addiere und subtrahiere

(\frac{1}{6})^{2}

x^{2} + \frac{x}{3} + 3 + (\frac{1}{6})^{2} - (\frac{1}{6})^{2}

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

x^{2} + \frac{1}{3} x + (\frac{1}{6})^{2} = (x + \frac{1}{6})^{2}

(x + \frac{1}{6})^{2} + 3 - (\frac{1}{6})^{2}

Vereinfache

(x + \frac{1}{6})^{2} + \frac{107}{36}

Graph

Beliebte Beispiele

x^{2} - 41 x + 400 = 0

solvefor x,x^2-xy+y^2=1

so l v e f or x, x^{2} - x y + y^{2} = 1

8 x - 1 = 4 x^{2}

x^{2} + 8 x + 35 = 0

4 x^{2} + x = 1