completesquare 3x^2+5x+3

Lösung

vervollständige das quadrat

3 x^{2} + 5 x + 3

3 (x + \frac{5}{6})^{2} + \frac{11}{12}

Schritte zur Lösung

3 x^{2} + 5 x + 3

Schreibe

3 x^{2} + 5 x + 3

in dieser Form:

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

Klammere aus

3

3 (x^{2} + \frac{5 x}{3} + 1)

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

Addiere und subtrahiere

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

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

Vereinfache

3 (x + \frac{5}{6})^{2} + \frac{11}{12}

3 x - 6 = - x^{2}

0.1 n^{2} + 100 n + 8 = 60000

so l v e f or x, x^{2} y^{3} = 6^{12}

3 x + 18 = x^{2}

so l v e f or y, y^{2} + 6 y + 9 = x + 8