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Beliebt Algebra >

completesquare 7/2 x^2+3x+8/3

Lösung

vervollständige das quadrat

\frac{7}{2} x^{2} + 3 x + \frac{8}{3}

Lösung

\frac{7}{2} (x + \frac{3}{7})^{2} + \frac{85}{42}

Schritte zur Lösung

\frac{7}{2} x^{2} + 3 x + \frac{8}{3}

Schreibe in der Standard Form

a x^{2} + b x + c

\frac{7 x ^{2}}{2} + 3 x + \frac{8}{3}

Schreibe

\frac{7 x ^{2}}{2} + 3 x + \frac{8}{3}

in dieser Form:

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

Klammere aus

\frac{7}{2}

\frac{7}{2} (x^{2} + \frac{6 x}{7} + \frac{16}{21})

2 a = \frac{6}{7} : a = \frac{3}{7}

Addiere und subtrahiere

(\frac{3}{7})^{2}

\frac{7}{2} (x^{2} + \frac{6 x}{7} + \frac{16}{21} + (\frac{3}{7})^{2} - (\frac{3}{7})^{2})

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

x^{2} + \frac{6}{7} x + (\frac{3}{7})^{2} = (x + \frac{3}{7})^{2}

\frac{7}{2} ((x + \frac{3}{7})^{2} + \frac{16}{21} - (\frac{3}{7})^{2})

Vereinfache

\frac{7}{2} (x + \frac{3}{7})^{2} + \frac{85}{42}

Graph

Beliebte Beispiele

27 - \frac{3}{4} x^{2} = 0

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X^{2} + 8 X + 15 = 0

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2 x^{2} + 6 x + 18 = 0