completesquare 3/4 x^2+x

Lösung

vervollständige das quadrat

\frac{3}{4} x^{2} + x

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

Schritte zur Lösung

\frac{3}{4} x^{2} + x

Schreibe in der Standard Form

a x^{2} + b x + c

\frac{3 x ^{2}}{4} + x

Schreibe

\frac{3 x ^{2}}{4} + x

in dieser Form:

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

Klammere aus

\frac{3}{4}

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

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

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

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

0 = - x^{2} + 5 x - 6

18 x^{2} - 144 x + 216 = 0

- 2 x^{2} - 18 x - 81 = - x^{2}

6 q^{2} - 8 q = 0

co m pl e t es q u a re x^{2} - 7 x + 2 = 0