completesquare 10x^2-19x+6

Lösung

vervollständige das quadrat

10 x^{2} - 19 x + 6

10 (x - \frac{19}{20})^{2} - \frac{121}{40}

Schritte zur Lösung

10 x^{2} - 19 x + 6

Schreibe

10 x^{2} - 19 x + 6

in dieser Form:

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

Klammere aus

10

10 (x^{2} - \frac{19 x}{10} + \frac{3}{5})

2 a = - \frac{19}{10} : a = - \frac{19}{20}

Addiere und subtrahiere

(- \frac{19}{20})^{2}

10 (x^{2} - \frac{19 x}{10} + \frac{3}{5} + (- \frac{19}{20})^{2} - (- \frac{19}{20})^{2})

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

x^{2} - \frac{19}{10} x + (- \frac{19}{20})^{2} = (x - \frac{19}{20})^{2}

10 ((x - \frac{19}{20})^{2} + \frac{3}{5} - (- \frac{19}{20})^{2})

Vereinfache

10 (x - \frac{19}{20})^{2} - \frac{121}{40}

2 x^{2} + 12 x + 6 = 0

x^{2} + 17 x + 70 = 0

x (x - 3) = 5 x + 1

co m pl e t es q u a re x^{2} - 4 x + 1 = 0

0 = - 4.9 t^{2} + 19.6 t + 58.8