completesquare x^2+1/3 x+5

Lösung

vervollständige das quadrat

x^{2} + \frac{1}{3} x + 5

(x + \frac{1}{6})^{2} + \frac{179}{36}

Schritte zur Lösung

x^{2} + \frac{1}{3} x + 5

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} + \frac{x}{3} + 5

Schreibe

x^{2} + \frac{x}{3} + 5

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} + 5 + (\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} + 5 - (\frac{1}{6})^{2}

Vereinfache

(x + \frac{1}{6})^{2} + \frac{179}{36}

- 2 x^{2} + 6 = 0

so l v e f or x, x^{2} - 2 x - 3 = 0

p^{2} - 16 p + 13 = - 3 p^{2}

(3 x - 4) (x + 5) = 0

x (x + 1) = 30