completesquare 3x^2-5x-2

Lösung

vervollständige das quadrat

3 x^{2} - 5 x - 2

3 (x - \frac{5}{6})^{2} - \frac{49}{12}

Schritte zur Lösung

3 x^{2} - 5 x - 2

Schreibe

3 x^{2} - 5 x - 2

in dieser Form:

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

Klammere aus

3

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

2 a = - \frac{5}{3} : a = - \frac{5}{6}

Addiere und subtrahiere

(- \frac{5}{6})^{2}

3 (x^{2} - \frac{5 x}{3} - \frac{2}{3} + (- \frac{5}{6})^{2} - (- \frac{5}{6})^{2})

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

x^{2} - \frac{5}{3} x + (- \frac{5}{6})^{2} = (x - \frac{5}{6})^{2}

3 ((x - \frac{5}{6})^{2} - \frac{2}{3} - (- \frac{5}{6})^{2})

Vereinfache

3 (x - \frac{5}{6})^{2} - \frac{49}{12}

m^{2} + 8 m + 15 = 0

x^{2} - 16 x - 36 = 0

co m pl e t es q u a re 3 x^{2} - 6 x - 5

3 x^{2} + 2 x = - 7

co m pl e t es q u a re x^{2} - 6 x + 5