completesquare 5x^2+9x+4

Lösung

vervollständige das quadrat

5 x^{2} + 9 x + 4

5 (x + \frac{9}{10})^{2} - \frac{1}{20}

Schritte zur Lösung

5 x^{2} + 9 x + 4

Schreibe

5 x^{2} + 9 x + 4

in dieser Form:

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

Klammere aus

5

5 (x^{2} + \frac{9 x}{5} + \frac{4}{5})

2 a = \frac{9}{5} : a = \frac{9}{10}

Addiere und subtrahiere

(\frac{9}{10})^{2}

5 (x^{2} + \frac{9 x}{5} + \frac{4}{5} + (\frac{9}{10})^{2} - (\frac{9}{10})^{2})

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

x^{2} + \frac{9}{5} x + (\frac{9}{10})^{2} = (x + \frac{9}{10})^{2}

5 ((x + \frac{9}{10})^{2} + \frac{4}{5} - (\frac{9}{10})^{2})

Vereinfache

5 (x + \frac{9}{10})^{2} - \frac{1}{20}

x^{2} - x + 30 = 0

co m pl e t es q u a re x^{2} - 4 x + 3

(x - 17)^{2} = 1

co m pl e t es q u a re s^{2} - 2 s + 2

5 x^{2} + 22 x + 2 = - 6