completesquare 4x^2-x-8

Lösung

vervollständige das quadrat

4 x^{2} - x - 8

4 (x - \frac{1}{8})^{2} - \frac{129}{16}

Schritte zur Lösung

4 x^{2} - x - 8

Schreibe

4 x^{2} - x - 8

in dieser Form:

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

Klammere aus

4

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

2 a = - \frac{1}{4} : a = - \frac{1}{8}

Addiere und subtrahiere

(- \frac{1}{8})^{2}

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

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

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

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

Vereinfache

4 (x - \frac{1}{8})^{2} - \frac{129}{16}

(x + 6) (x - 1) = - 10

co m pl e t es q u a re 4 x^{2} + 2 x + 5

5 x^{2} + 31623 x + 50 = 0

- 4.9 t^{2} + 18 t + 7.4 = 0

4 (x + 5)^{2} + 6 = 54