completesquare x^2+2/5 x+9

Lösung

vervollständige das quadrat

x^{2} + \frac{2}{5} x + 9

(x + \frac{1}{5})^{2} + \frac{224}{25}

Schritte zur Lösung

x^{2} + \frac{2}{5} x + 9

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} + \frac{2 x}{5} + 9

Schreibe

x^{2} + \frac{2 x}{5} + 9

in dieser Form:

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

2 a = \frac{2}{5} : a = \frac{1}{5}

Addiere und subtrahiere

(\frac{1}{5})^{2}

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

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

x^{2} + \frac{2}{5} x + (\frac{1}{5})^{2} = (x + \frac{1}{5})^{2}

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

Vereinfache

(x + \frac{1}{5})^{2} + \frac{224}{25}

x^{2} + 22 x + 28 = 12 x

2 x^{2} - 5 x - 3 = 2 x - 4 x^{2}

2 (2 x + 1)^{2} = (x + 3)^{2} - 10

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

9 x^{2} - 6 x + 7 = 0