completesquare x^2-1/2 x

Lösung

vervollständige das quadrat

x^{2} - \frac{1}{2} x

(x - \frac{1}{4})^{2} - \frac{1}{16}

Schritte zur Lösung

x^{2} - \frac{1}{2} x

Schreibe in der Standard Form

a x^{2} + b x + c

x^{2} - \frac{x}{2}

Schreibe

x^{2} - \frac{x}{2}

in dieser Form:

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

2 a = - \frac{1}{2} : a = - \frac{1}{4}

Addiere und subtrahiere

(- \frac{1}{4})^{2}

x^{2} - \frac{x}{2} + (- \frac{1}{4})^{2} - (- \frac{1}{4})^{2}

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

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

(x - \frac{1}{4})^{2} - (- \frac{1}{4})^{2}

Vereinfache

(x - \frac{1}{4})^{2} - \frac{1}{16}

(3 x - 5)^{2} = 49

co m pl e t es q u a re x^{2} - 6 x + 10 = 0

2 x^{2} + 14 x + 3 = - 17

2 x^{2} - 14 x + 1 = 0

co m pl e t es q u a re x^{2} - 4 x = 0