completesquare 3x^2+2x-7

Lösung

vervollständige das quadrat

3 x^{2} + 2 x - 7

3 (x + \frac{1}{3})^{2} - \frac{22}{3}

Schritte zur Lösung

3 x^{2} + 2 x - 7

Schreibe

3 x^{2} + 2 x - 7

in dieser Form:

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

Klammere aus

3

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

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

Addiere und subtrahiere

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

3 (x^{2} + \frac{2 x}{3} - \frac{7}{3} + (\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}

3 ((x + \frac{1}{3})^{2} - \frac{7}{3} - (\frac{1}{3})^{2})

Vereinfache

3 (x + \frac{1}{3})^{2} - \frac{22}{3}

3 x^{2} = 19 x - 20

(3 + x) \frac{2}{m} + 6 (3 - x) \frac{2}{m} = 5 (9 - x^{2}) \frac{1}{m}

(x + 3)^{2} - 81 = 0

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

x^{2} + 11 x - 80 = 0