completesquare 4x^2+5x+2

Lösung

vervollständige das quadrat

4 x^{2} + 5 x + 2

4 (x + \frac{5}{8})^{2} + \frac{7}{16}

Schritte zur Lösung

4 x^{2} + 5 x + 2

Schreibe

4 x^{2} + 5 x + 2

in dieser Form:

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

Klammere aus

4

4 (x^{2} + \frac{5 x}{4} + \frac{1}{2})

2 a = \frac{5}{4} : a = \frac{5}{8}

Addiere und subtrahiere

(\frac{5}{8})^{2}

4 (x^{2} + \frac{5 x}{4} + \frac{1}{2} + (\frac{5}{8})^{2} - (\frac{5}{8})^{2})

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

x^{2} + \frac{5}{4} x + (\frac{5}{8})^{2} = (x + \frac{5}{8})^{2}

4 ((x + \frac{5}{8})^{2} + \frac{1}{2} - (\frac{5}{8})^{2})

Vereinfache

4 (x + \frac{5}{8})^{2} + \frac{7}{16}

x^{2} + 3 x = 5 x + 3

so l v e f or x, x^{2} + 2 y^{2} = k^{2}

3 x^{2} + 12 x + 14 = 0

12 x^{2} - 128 x + 231 = 0

2 x^{2} - 15 x + 25 = 0