completesquare x^2+4/5 x-8

Lösung

vervollständige das quadrat

x^{2} + \frac{4}{5} x - 8

(x + \frac{2}{5})^{2} - \frac{204}{25}

Schritte zur Lösung

x^{2} + \frac{4}{5} x - 8

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} + \frac{4 x}{5} - 8

Schreibe

x^{2} + \frac{4 x}{5} - 8

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

Vereinfache

(x + \frac{2}{5})^{2} - \frac{204}{25}

25 x^{2} - 5625 = 0

(m - 2)^{2} = 5 - 2 (2 m + 7) + 6^{2} + 2

2 x (x - 2) = x^{2} - 10

3 x^{2} + 1 = - 2 x

5 x^{2} = 405