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}

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

x (x - a) - b (a + b) = 0

z^{2} - 5 z + 84 = 0

x^{2} - 13 x + 6 = 0

2 x^{2} + x - 20 = - 2 x^{2}