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Beliebt Algebra >

completesquare x^2+1/2 x+3

Lösung

vervollständige das quadrat

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

Lösung

(x + \frac{1}{4})^{2} + \frac{47}{16}

Schritte zur Lösung

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

Schreibe in der Standard Form

a x^{2} + b x + c

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

Schreibe

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

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} + 3 + (\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} + 3 - (\frac{1}{4})^{2}

Vereinfache

(x + \frac{1}{4})^{2} + \frac{47}{16}

Graph

Beliebte Beispiele

x^{2} - 3 x + 2 = 2

4(x^2-4)-5(3+2x)=-7

4 (x^{2} - 4) - 5 (3 + 2 x) = - 7

(x - 7) (x + 4) = 0

2 x^{2} + 10 x + 4 = 0

4 x^{2} + 6 x + 3 = 0