completesquare 5x^2+3x-4

Lösung

vervollständige das quadrat

5 x^{2} + 3 x - 4

5 (x + \frac{3}{10})^{2} - \frac{89}{20}

Schritte zur Lösung

5 x^{2} + 3 x - 4

Schreibe

5 x^{2} + 3 x - 4

in dieser Form:

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

Klammere aus

5

5 (x^{2} + \frac{3 x}{5} - \frac{4}{5})

2 a = \frac{3}{5} : a = \frac{3}{10}

Addiere und subtrahiere

(\frac{3}{10})^{2}

5 (x^{2} + \frac{3 x}{5} - \frac{4}{5} + (\frac{3}{10})^{2} - (\frac{3}{10})^{2})

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

x^{2} + \frac{3}{5} x + (\frac{3}{10})^{2} = (x + \frac{3}{10})^{2}

5 ((x + \frac{3}{10})^{2} - \frac{4}{5} - (\frac{3}{10})^{2})

Vereinfache

5 (x + \frac{3}{10})^{2} - \frac{89}{20}

co m pl e t es q u a re x^{2} + 10

17 = b^{2}

- 10 x^{2} - 7 x + 12 = 0

6 x^{2} - 7 x - 3 = - 8 x - 1

192 = 128 t - 16 t^{2}