completesquare-x^2+9x-3

Lösung

vervollständige das quadrat

- x^{2} + 9 x - 3

- (x - \frac{9}{2})^{2} + \frac{69}{4}

Schritte zur Lösung

- x^{2} + 9 x - 3

Schreibe

- x^{2} + 9 x - 3

in dieser Form:

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

Klammere aus

- 1

- (x^{2} - 9 x + 3)

2 a = - 9 : a = - \frac{9}{2}

Addiere und subtrahiere

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

- (x^{2} - 9 x + 3 + (- \frac{9}{2})^{2} - (- \frac{9}{2})^{2})

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

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

- ((x - \frac{9}{2})^{2} + 3 - (- \frac{9}{2})^{2})

Vereinfache

- (x - \frac{9}{2})^{2} + \frac{69}{4}

(x - 2) (x - 3) = 30

7 x + 2 (- 9 x + 3) = x - (- 4 x + 6) x - (- 4 x + 6)

so l v e f or x, x^{2} + 2 x y + y^{2} = 64

x^{2} + 5 = 5 \frac{1}{16}

x^{2} + \frac{x}{2} + 1 = 0