completesquare x^2-4/5 x-1

Lösung

vervollständige das quadrat

x^{2} - \frac{4}{5} x - 1

(x - \frac{2}{5})^{2} - \frac{29}{25}

Schritte zur Lösung

x^{2} - \frac{4}{5} x - 1

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} - \frac{4 x}{5} - 1

Schreibe

x^{2} - \frac{4 x}{5} - 1

in dieser Form:

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

2 a = - \frac{4}{5} : a = - \frac{2}{5}

Addiere und subtrahiere

(- \frac{2}{5})^{2}

x^{2} - \frac{4 x}{5} - 1 + (- \frac{2}{5})^{2} - (- \frac{2}{5})^{2}

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

x^{2} - \frac{4}{5} x + (- \frac{2}{5})^{2} = (x - \frac{2}{5})^{2}

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

Vereinfache

(x - \frac{2}{5})^{2} - \frac{29}{25}

co m pl e t es q u a re z^{2} - 2 z

z^{2} + 3 z - 7 = z

co m pl e t es q u a re x^{2} + 2 x - 8 = 0

3 x^{2} - 7 = 5

7 k = 78 - k^{2}