completesquare 1/9000 x^2-7/15 x+500

Lösung

vervollständige das quadrat

\frac{1}{9000} x^{2} - \frac{7}{15} x + 500

\frac{1}{9000} (x - 2100)^{2} + 10

Schritte zur Lösung

\frac{1}{9000} x^{2} - \frac{7}{15} x + 500

Schreibe in der Standard Form

a x^{2} + b x + c

\frac{x ^{2}}{9000} - \frac{7 x}{15} + 500

Schreibe

\frac{x ^{2}}{9000} - \frac{7 x}{15} + 500

in dieser Form:

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

Klammere aus

\frac{1}{9000}

\frac{1}{9000} (x^{2} - 4200 x + 4500000)

2 a = - 4200 : a = - 2100

Addiere und subtrahiere

(- 2100)^{2}

\frac{1}{9000} (x^{2} - 4200 x + 4500000 + (- 2100)^{2} - (- 2100)^{2})

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

x^{2} - 4200 x + (- 2100)^{2} = (x - 2100)^{2}

\frac{1}{9000} ((x - 2100)^{2} + 4500000 - (- 2100)^{2})

Vereinfache

\frac{1}{9000} (x - 2100)^{2} + 10

f a c t or x^{2} + 10 x = 0

100 x^{2} + 20 x + 1 = 0

5 x^{2} - 27 x - 18 = 0

x^{2} + (x + 14)^{2} = 3 4^{2}

X^{2} + 5 X - 14 = 0