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Beliebt Algebra >

completesquare 1/2 x^2+4x

Lösung

vervollständige das quadrat

\frac{1}{2} x^{2} + 4 x

Lösung

\frac{1}{2} (x + 4)^{2} - 8

Schritte zur Lösung

\frac{1}{2} x^{2} + 4 x

Schreibe in der Standard Form

a x^{2} + b x + c

\frac{x ^{2}}{2} + 4 x

Schreibe

\frac{x ^{2}}{2} + 4 x

in dieser Form:

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

Klammere aus

\frac{1}{2}

\frac{1}{2} (x^{2} + 8 x)

2 a = 8 : a = 4

Addiere und subtrahiere

4^{2}

\frac{1}{2} (x^{2} + 8 x + 4^{2} - 4^{2})

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

x^{2} + 8 x + 4^{2} = (x + 4)^{2}

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

Vereinfache

\frac{1}{2} (x + 4)^{2} - 8

Graph

Beliebte Beispiele

x^{2} - 10 = 15

x^2=(x-1)^2+(x-2)^2

x^{2} = (x - 1)^{2} + (x - 2)^{2}

10 x = - 25 - x^{2}

x^{2} + 7 x + 30 = 18

6x^2+12x+14=7x^2-5

6 x^{2} + 12 x + 14 = 7 x^{2} - 5