completesquare-3x^2+9x+5

Lösung

vervollständige das quadrat

- 3 x^{2} + 9 x + 5

- 3 (x - \frac{3}{2})^{2} + \frac{47}{4}

Schritte zur Lösung

- 3 x^{2} + 9 x + 5

Schreibe

- 3 x^{2} + 9 x + 5

in dieser Form:

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

Klammere aus

- 3

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

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

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

- 3 (x - \frac{3}{2})^{2} + \frac{47}{4}

6 a^{2} + 2 a - 113 = - 9

x \frac{4 x - 3}{5} - \frac{2 x - 3}{2} = - 2

9 x (x + 1) 2 - 4 = 0

p^{2} - 2 p - 48 = 0

x^{2} - 5 x - 1 = - 5