completesquare 2x^2-3x+1

Lösung

vervollständige das quadrat

2 x^{2} - 3 x + 1

2 (x - \frac{3}{4})^{2} - \frac{1}{8}

Schritte zur Lösung

2 x^{2} - 3 x + 1

Schreibe

2 x^{2} - 3 x + 1

in dieser Form:

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

Klammere aus

2

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

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

Addiere und subtrahiere

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

2 (x^{2} - \frac{3 x}{2} + \frac{1}{2} + (- \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}

2 ((x - \frac{3}{4})^{2} + \frac{1}{2} - (- \frac{3}{4})^{2})

Vereinfache

2 (x - \frac{3}{4})^{2} - \frac{1}{8}

x^{2} + 8 x - 192 = 0

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

co m pl e t es q u a re v^{2} + 8 v

X^{2} - 10 X + 25 = 0

so l v e f or x, f = 10 x^{2} ln (5 y + 3 z)