completesquare 8z^2+5z

Lösung

vervollständige das quadrat

8 z^{2} + 5 z

8 (z + \frac{5}{16})^{2} - \frac{25}{32}

Schritte zur Lösung

8 z^{2} + 5 z

Schreibe

8 z^{2} + 5 z

in dieser Form:

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

Klammere aus

8

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

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

Addiere und subtrahiere

(\frac{5}{16})^{2}

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

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

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

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

Vereinfache

8 (z + \frac{5}{16})^{2} - \frac{25}{32}

so l v e f or x, (x - 3)^{2} + (y - 5)^{2} = 0

q u a d r a t i c f or m u l a x^{2} + 11 x + 24 = 0

18 k^{2} = 50

co m pl e t es q u a re x^{2} - 10 x - 3

(x - 1) (x + 2) = 4