completesquare x^2+2/3 x

Lösung

vervollständige das quadrat

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

(x + \frac{1}{3})^{2} - \frac{1}{9}

Schritte zur Lösung

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

Schreibe in der Standard Form

a x^{2} + b x + c

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

Schreibe

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

in dieser Form:

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

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

Addiere und subtrahiere

(\frac{1}{3})^{2}

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

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

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

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

Vereinfache

(x + \frac{1}{3})^{2} - \frac{1}{9}

\frac{1}{10} x^{2} - 10 = 0

x^{(2)} - 3 x + 2 = e^{(3)}

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

so l v e f or x, y = \frac{1}{4} x^{2}

x^{2} - 5 + 4 = 0