completesquare 3x^2-9x+8

Lösung

vervollständige das quadrat

3 x^{2} - 9 x + 8

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

Schritte zur Lösung

3 x^{2} - 9 x + 8

Schreibe

3 x^{2} - 9 x + 8

in dieser Form:

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

Klammere aus

3

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

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

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

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

co m pl e t es q u a re x (x + 3) = 5 x + 3

(1 - x) (3 - x) - 8 = 0

so l v e f or x, x^{2} - 4 x - 3 = 0

co m pl e t es q u a re 7 x^{2} + 84 x + 247

(2 x - 5)^{2} + 4 x = 12