completesquare 9+5x-x^2

Lösung

vervollständige das quadrat

9 + 5 x - x^{2}

- (x - \frac{5}{2})^{2} + \frac{61}{4}

Schritte zur Lösung

9 + 5 x - x^{2}

Schreibe in der Standard Form

a x^{2} + b x + c

- x^{2} + 5 x + 9

Schreibe

- x^{2} + 5 x + 9

in dieser Form:

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

Klammere aus

- 1

- (x^{2} - 5 x - 9)

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

Addiere und subtrahiere

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

- (x^{2} - 5 x - 9 + (- \frac{5}{2})^{2} - (- \frac{5}{2})^{2})

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

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

- ((x - \frac{5}{2})^{2} - 9 - (- \frac{5}{2})^{2})

Vereinfache

- (x - \frac{5}{2})^{2} + \frac{61}{4}

so l v e f or x, x^{2} (y + 4)^{2} = 25

- 2 (x + 1)^{2} - 4 = 12

- 6 x^{2} + 4 = 0

4^{2} = x^{2} + 3^{2}

0 = \frac{2}{3} x^{2} - 6 x + 12