completesquare x^2-4/5 x-4

Lösung

vervollständige das quadrat

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

(x - \frac{2}{5})^{2} - \frac{104}{25}

Schritte zur Lösung

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

Schreibe in der Standard Form

a x^{2} + b x + c

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

Schreibe

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

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

Vereinfache

(x - \frac{2}{5})^{2} - \frac{104}{25}

a^{2} - a + 1 = 0

6 x^{2} = 13 x + 15

7 - \frac{1}{4} x^{2} - \frac{4}{3} x = 0

co m pl e t es q u a re 2 x^{2} + 4 x + 3

8 r^{2} - 2 r - 7 = 6 r^{2}