completesquare 4x^2+36x+31

Lösung

vervollständige das quadrat

4 x^{2} + 36 x + 31

4 (x + \frac{9}{2})^{2} - 50

Schritte zur Lösung

4 x^{2} + 36 x + 31

Schreibe

4 x^{2} + 36 x + 31

in dieser Form:

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

Klammere aus

4

4 (x^{2} + 9 x + \frac{31}{4})

2 a = 9 : a = \frac{9}{2}

Addiere und subtrahiere

(\frac{9}{2})^{2}

4 (x^{2} + 9 x + \frac{31}{4} + (\frac{9}{2})^{2} - (\frac{9}{2})^{2})

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

x^{2} + 9 x + (\frac{9}{2})^{2} = (x + \frac{9}{2})^{2}

4 ((x + \frac{9}{2})^{2} + \frac{31}{4} - (\frac{9}{2})^{2})

Vereinfache

4 (x + \frac{9}{2})^{2} - 50

15 x^{2} - 6 = - 13 x

so l v e f or x, x^{2} + 9 b^{2} = 0

4 x (2 x - 1) - x = 3

co m pl e t es q u a re 2 x^{2} + 4 x - 1

so l v e f or x, v + w = x^{2} yz