completesquare 4x^2+3x+2

Lösung

vervollständige das quadrat

4 x^{2} + 3 x + 2

4 (x + \frac{3}{8})^{2} + \frac{23}{16}

Schritte zur Lösung

4 x^{2} + 3 x + 2

Schreibe

4 x^{2} + 3 x + 2

in dieser Form:

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

Klammere aus

4

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

2 a = \frac{3}{4} : a = \frac{3}{8}

Addiere und subtrahiere

(\frac{3}{8})^{2}

4 (x^{2} + \frac{3 x}{4} + \frac{1}{2} + (\frac{3}{8})^{2} - (\frac{3}{8})^{2})

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

x^{2} + \frac{3}{4} x + (\frac{3}{8})^{2} = (x + \frac{3}{8})^{2}

4 ((x + \frac{3}{8})^{2} + \frac{1}{2} - (\frac{3}{8})^{2})

Vereinfache

4 (x + \frac{3}{8})^{2} + \frac{23}{16}

2 x^{2} + 11 x = - 12

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

0 = - x^{2} + 5 x - 6

18 x^{2} - 144 x + 216 = 0

- 2 x^{2} - 18 x - 81 = - x^{2}