completesquare (5*x)/8+(x^2)/(51)

Lösung

vervollständige das quadrat

\frac{5 \cdot x}{8} + \frac{x ^{2}}{51}

\frac{1}{51} (x + \frac{255}{16})^{2} - \frac{1275}{256}

Schritte zur Lösung

\frac{5 x}{8} + \frac{x ^{2}}{51}

Schreibe in der Standard Form

a x^{2} + b x + c

\frac{1 \cdot x ^{2}}{51} + \frac{5 x}{8}

Schreibe

\frac{1 x ^{2}}{51} + \frac{5 x}{8}

in dieser Form:

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

Klammere aus

\frac{1}{51}

\frac{1}{51} (x^{2} + \frac{255 x}{8})

2 a = \frac{255}{8} : a = \frac{255}{16}

Addiere und subtrahiere

(\frac{255}{16})^{2}

\frac{1}{51} (x^{2} + \frac{255 x}{8} + (\frac{255}{16})^{2} - (\frac{255}{16})^{2})

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

x^{2} + \frac{255}{8} x + (\frac{255}{16})^{2} = (x + \frac{255}{16})^{2}

\frac{1}{51} ((x + \frac{255}{16})^{2} - (\frac{255}{16})^{2})

Vereinfache

\frac{1}{51} (x + \frac{255}{16})^{2} - \frac{1275}{256}

- 160 x^{2} + 450 x - 300 = 0

g (g + 10) = - 6

1000 x \cdot \frac{x}{2} = 5643 (104 - x)

9^{2} + 1 5^{2} = c^{2}

1200 - 280 x + 12 x^{2} = 0