completesquare 2x^2-7x+4

Lösung

vervollständige das quadrat

2 x^{2} - 7 x + 4

2 (x - \frac{7}{4})^{2} - \frac{17}{8}

Schritte zur Lösung

2 x^{2} - 7 x + 4

Schreibe

2 x^{2} - 7 x + 4

in dieser Form:

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

Klammere aus

2

2 (x^{2} - \frac{7 x}{2} + 2)

2 a = - \frac{7}{2} : a = - \frac{7}{4}

Addiere und subtrahiere

(- \frac{7}{4})^{2}

2 (x^{2} - \frac{7 x}{2} + 2 + (- \frac{7}{4})^{2} - (- \frac{7}{4})^{2})

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

x^{2} - \frac{7}{2} x + (- \frac{7}{4})^{2} = (x - \frac{7}{4})^{2}

2 ((x - \frac{7}{4})^{2} + 2 - (- \frac{7}{4})^{2})

Vereinfache

2 (x - \frac{7}{4})^{2} - \frac{17}{8}

r^{2} - 6 r + 12 = 0

(1 - k) x^{2} + x + k = 0

2 x^{2} - 19 x - 10 = 0

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

f a c t or x^{2} - 4 x = 77