completesquare 2x^2+3x+1

Lösung

vervollständige das quadrat

2 x^{2} + 3 x + 1

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

Schritte zur Lösung

2 x^{2} + 3 x + 1

Schreibe

2 x^{2} + 3 x + 1

in dieser Form:

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

Klammere aus

2

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

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

Addiere und subtrahiere

(\frac{3}{4})^{2}

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

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

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

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

Vereinfache

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

x^{2} + 6 = 55

so l v e f or x, x^{2} y^{3} + 4 x y + x - 6 y = 2

x^{2} + 3 x + 1 = 1

- x^{2} - 3 x + 6 = 3 - x

x^{2} + 11 x + 13 = 33