completesquare 3x^2+4x+1

Lösung

vervollständige das quadrat

3 x^{2} + 4 x + 1

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

Schritte zur Lösung

3 x^{2} + 4 x + 1

Schreibe

3 x^{2} + 4 x + 1

in dieser Form:

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

Klammere aus

3

3 (x^{2} + \frac{4 x}{3} + \frac{1}{3})

2 a = \frac{4}{3} : a = \frac{2}{3}

Addiere und subtrahiere

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

3 (x^{2} + \frac{4 x}{3} + \frac{1}{3} + (\frac{2}{3})^{2} - (\frac{2}{3})^{2})

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

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

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

Vereinfache

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

co m pl e t es q u a re 3 x^{2} + 4 x - 3

\frac{g ^{2}}{200} (114 + 115) = 20

- \frac{1}{4} x^{2} - 2 x - 4 = 0

4 p^{2} - 8 p - 5 = 0

2 v^{2} + 9 v + 9 = 0