completesquare 3x^2-5x-7

Lösung

vervollständige das quadrat

3 x^{2} - 5 x - 7

3 (x - \frac{5}{6})^{2} - \frac{109}{12}

Schritte zur Lösung

3 x^{2} - 5 x - 7

Schreibe

3 x^{2} - 5 x - 7

in dieser Form:

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

Klammere aus

3

3 (x^{2} - \frac{5 x}{3} - \frac{7}{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{7}{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{7}{3} - (- \frac{5}{6})^{2})

Vereinfache

3 (x - \frac{5}{6})^{2} - \frac{109}{12}

8 x^{2} - 10 x - 5 = 0

co m pl e t es q u a re 2 s^{2} + 3.6 s + 15

16 - 4 x = 8 x^{2}

x^{2} + 3 x + c = \frac{7}{4} + c

7 x^{2} + x - 8 = 0