completesquare-3x^2-7x+5

Lösung

vervollständige das quadrat

- 3 x^{2} - 7 x + 5

- 3 (x + \frac{7}{6})^{2} + \frac{109}{12}

Schritte zur Lösung

- 3 x^{2} - 7 x + 5

Schreibe

- 3 x^{2} - 7 x + 5

in dieser Form:

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

Klammere aus

- 3

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

2 a = \frac{7}{3} : a = \frac{7}{6}

Addiere und subtrahiere

(\frac{7}{6})^{2}

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

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

x^{2} + \frac{7}{3} x + (\frac{7}{6})^{2} = (x + \frac{7}{6})^{2}

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

Vereinfache

- 3 (x + \frac{7}{6})^{2} + \frac{109}{12}

60 x^{2} - 180 x = 0

so l v e f or f, f^{- 1} (x) = x^{2} - 2

so l v e f or f, f^{- 1} (x) = x^{2} - 4

d^{2} = 4 (3 d + 7)

- 2 x^{2} - 12 x - 8 = 0