completesquare x-2x^2

Lösung

vervollständige das quadrat

x - 2 x^{2}

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

Schritte zur Lösung

x - 2 x^{2}

Schreibe in der Standard Form

a x^{2} + b x + c

- 2 x^{2} + x

Schreibe

- 2 x^{2} + x

in dieser Form:

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

Klammere aus

- 2

- 2 (x^{2} - \frac{x}{2})

2 a = - \frac{1}{2} : a = - \frac{1}{4}

Addiere und subtrahiere

(- \frac{1}{4})^{2}

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

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

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

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

Vereinfache

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

39 x^{2} = 91

f a c t or 2 x^{2} + 5 x - 7 = 0

so l v e f or y, y^{2} = x^{3} - 8 x

4 x (x - 4) = 1

3 x^{2} - 420 = 0