completesquare 2x^2-1/3 x

Lösung

vervollständige das quadrat

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

2 (x - \frac{1}{12})^{2} - \frac{1}{72}

Schritte zur Lösung

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

Schreibe in der Standard Form

a x^{2} + b x + c

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

Schreibe

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

in dieser Form:

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

Klammere aus

2

2 (x^{2} - \frac{x}{6})

2 a = - \frac{1}{6} : a = - \frac{1}{12}

Addiere und subtrahiere

(- \frac{1}{12})^{2}

2 (x^{2} - \frac{x}{6} + (- \frac{1}{12})^{2} - (- \frac{1}{12})^{2})

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

x^{2} - \frac{1}{6} x + (- \frac{1}{12})^{2} = (x - \frac{1}{12})^{2}

2 ((x - \frac{1}{12})^{2} - (- \frac{1}{12})^{2})

Vereinfache

2 (x - \frac{1}{12})^{2} - \frac{1}{72}

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

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

5 z - 5 z^{2} = 1.2

w^{2} + 3 w + 2 = 0

f a c t or x^{2} - 14 = 5 x