completesquare 9x^2-6x+2

Lösung

vervollständige das quadrat

9 x^{2} - 6 x + 2

9 (x - \frac{1}{3})^{2} + 1

Schritte zur Lösung

9 x^{2} - 6 x + 2

Schreibe

9 x^{2} - 6 x + 2

in dieser Form:

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

Klammere aus

9

9 (x^{2} - \frac{2 x}{3} + \frac{2}{9})

2 a = - \frac{2}{3} : a = - \frac{1}{3}

Addiere und subtrahiere

(- \frac{1}{3})^{2}

9 (x^{2} - \frac{2 x}{3} + \frac{2}{9} + (- \frac{1}{3})^{2} - (- \frac{1}{3})^{2})

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

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

9 ((x - \frac{1}{3})^{2} + \frac{2}{9} - (- \frac{1}{3})^{2})

Vereinfache

9 (x - \frac{1}{3})^{2} + 1

m^{2} + 10 m - 17 = 0

2 x^{2} - 44 x + 224 = 0

co m pl e t es q u a re x^{2} - 8 x - 1 = 0

so l v e f or t, s t + t = t^{2} + s

y^{2} - 18 y + 45 = 0