completesquare x^2-1/5 x-6

Lösung

vervollständige das quadrat

x^{2} - \frac{1}{5} x - 6

(x - \frac{1}{10})^{2} - \frac{601}{100}

Schritte zur Lösung

x^{2} - \frac{1}{5} x - 6

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} - \frac{x}{5} - 6

Schreibe

x^{2} - \frac{x}{5} - 6

in dieser Form:

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

2 a = - \frac{1}{5} : a = - \frac{1}{10}

Addiere und subtrahiere

(- \frac{1}{10})^{2}

x^{2} - \frac{x}{5} - 6 + (- \frac{1}{10})^{2} - (- \frac{1}{10})^{2}

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

x^{2} - \frac{1}{5} x + (- \frac{1}{10})^{2} = (x - \frac{1}{10})^{2}

(x - \frac{1}{10})^{2} - 6 - (- \frac{1}{10})^{2}

Vereinfache

(x - \frac{1}{10})^{2} - \frac{601}{100}

x^{2} - 13 = 4 x

3 x^{2} = - 1

X^{2} - 36 = 0

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

5 x^{2} + 17 x - 12 = 0