completesquare 2x^2+7x+6

Lösung

vervollständige das quadrat

2 x^{2} + 7 x + 6

2 (x + \frac{7}{4})^{2} - \frac{1}{8}

Schritte zur Lösung

2 x^{2} + 7 x + 6

Schreibe

2 x^{2} + 7 x + 6

in dieser Form:

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

Klammere aus

2

2 (x^{2} + \frac{7 x}{2} + 3)

2 a = \frac{7}{2} : a = \frac{7}{4}

Addiere und subtrahiere

(\frac{7}{4})^{2}

2 (x^{2} + \frac{7 x}{2} + 3 + (\frac{7}{4})^{2} - (\frac{7}{4})^{2})

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

x^{2} + \frac{7}{2} x + (\frac{7}{4})^{2} = (x + \frac{7}{4})^{2}

2 ((x + \frac{7}{4})^{2} + 3 - (\frac{7}{4})^{2})

Vereinfache

2 (x + \frac{7}{4})^{2} - \frac{1}{8}

4 x^{2} + 7 x - 4 = 0

co m pl e t es q u a re n^{2} = 18 n + 40

so l v e f or x, x^{2} + 3 x + 4 = m x

8 x^{2} - 50 = 0

so l v e f or x, z = x^{2} e^{- y}