completesquare 5x^2+8x+2

Lösung

vervollständige das quadrat

5 x^{2} + 8 x + 2

5 (x + \frac{4}{5})^{2} - \frac{6}{5}

Schritte zur Lösung

5 x^{2} + 8 x + 2

Schreibe

5 x^{2} + 8 x + 2

in dieser Form:

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

Klammere aus

5

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

2 a = \frac{8}{5} : a = \frac{4}{5}

Addiere und subtrahiere

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

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

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

x^{2} + \frac{8}{5} x + (\frac{4}{5})^{2} = (x + \frac{4}{5})^{2}

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

Vereinfache

5 (x + \frac{4}{5})^{2} - \frac{6}{5}

x^{2} = (x - 2) (x - 2 + x - 1)

3 x^{2} - 2 x - 21 = 0

so l v e f or r, s = 4 π r^{2}

x^{2} - 12 x + 36 = 44

co m pl e t es q u a re 5 x^{2} + 9 x + 4