completesquare-8x^2+(8sqrt(10))/5 x

Lösung

vervollständige das quadrat

- 8 x^{2} + \frac{8 10}{5} x

- 8 (x - \frac{1}{10})^{2} + \frac{4}{5}

Schritte zur Lösung

- 8 x^{2} + \frac{8 10}{5} x

Schreibe in der Standard Form

a x^{2} + b x + c

- 8 x^{2} + \frac{8 2 x}{5}

Schreibe

- 8 x^{2} + \frac{8 2 x}{5}

in dieser Form:

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

Klammere aus

- 8

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

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

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

- 8 (x - \frac{1}{10})^{2} + \frac{4}{5}

so l v e f or x, x^{2} + 4 y^{2} + 9 z^{2} = 1

co m pl e t es q u a re x^{2} + 17 x

- 3 x^{2} - 18 x = 0

1 - 2 x - x^{2} = 0

- 6 x^{2} + 84 x - 240 = 0