completesquare 5y^2+16y+64

Lösung

vervollständige das quadrat

5 y^{2} + 16 y + 64

5 (y + \frac{8}{5})^{2} + \frac{256}{5}

Schritte zur Lösung

5 y^{2} + 16 y + 64

Schreibe

5 y^{2} + 16 y + 64

in dieser Form:

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

Klammere aus

5

5 (y^{2} + \frac{16 y}{5} + \frac{64}{5})

2 a = \frac{16}{5} : a = \frac{8}{5}

Addiere und subtrahiere

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

5 (y^{2} + \frac{16 y}{5} + \frac{64}{5} + (\frac{8}{5})^{2} - (\frac{8}{5})^{2})

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

y^{2} + \frac{16}{5} y + (\frac{8}{5})^{2} = (y + \frac{8}{5})^{2}

5 ((y + \frac{8}{5})^{2} + \frac{64}{5} - (\frac{8}{5})^{2})

Vereinfache

5 (y + \frac{8}{5})^{2} + \frac{256}{5}

- 9 x^{2} + 40 x + 84 = 0

x^{2} - 12 x + 100 = 80

x^{2} = 3 + 2 x

x^{2} + 0.1 x + 0.0018 = 0

m x^{2} - 2 (m - 1) x + 3 m - 1 = 0