completesquare-2x^2+5x+3

Lösung

vervollständige das quadrat

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

- 2 (x - \frac{5}{4})^{2} + \frac{49}{8}

Schritte zur Lösung

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

Schreibe

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

in dieser Form:

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

Klammere aus

- 2

- 2 (x^{2} - \frac{5 x}{2} - \frac{3}{2})

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

Addiere und subtrahiere

(- \frac{5}{4})^{2}

- 2 (x^{2} - \frac{5 x}{2} - \frac{3}{2} + (- \frac{5}{4})^{2} - (- \frac{5}{4})^{2})

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

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

- 2 ((x - \frac{5}{4})^{2} - \frac{3}{2} - (- \frac{5}{4})^{2})

Vereinfache

- 2 (x - \frac{5}{4})^{2} + \frac{49}{8}

5.400447427 x^{2} + 8.145 x - 41.59 = 0

6 x^{2} = - 11 x + 10

12 - 3 y^{2} = 0

(2 x - 3) \cdot (2 x + 3) + 2 x - 35 = 100 + 2 x

x^{2} - 3 = 7