completesquare 4x^2-6x+9

Lösung

vervollständige das quadrat

4 x^{2} - 6 x + 9

4 (x - \frac{3}{4})^{2} + \frac{27}{4}

Schritte zur Lösung

4 x^{2} - 6 x + 9

Schreibe

4 x^{2} - 6 x + 9

in dieser Form:

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

Klammere aus

4

4 (x^{2} - \frac{3 x}{2} + \frac{9}{4})

2 a = - \frac{3}{2} : a = - \frac{3}{4}

Addiere und subtrahiere

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

4 (x^{2} - \frac{3 x}{2} + \frac{9}{4} + (- \frac{3}{4})^{2} - (- \frac{3}{4})^{2})

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

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

4 ((x - \frac{3}{4})^{2} + \frac{9}{4} - (- \frac{3}{4})^{2})

Vereinfache

4 (x - \frac{3}{4})^{2} + \frac{27}{4}

(- \frac{3}{2})^{2} + (\frac{1}{2})^{2} = r^{2}

co m pl e t es q u a re 3 x^{2} - 6 x + 2 = 0

2 x^{2} - 8 = 41

3 x^{2} - x - 48 = 0

2 z^{2} + 3 z - 6 = 0