completesquare 7x^2+4x

Lösung

vervollständige das quadrat

7 x^{2} + 4 x

7 (x + \frac{2}{7})^{2} - \frac{4}{7}

Schritte zur Lösung

7 x^{2} + 4 x

Schreibe

7 x^{2} + 4 x

in dieser Form:

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

Klammere aus

7

7 (x^{2} + \frac{4 x}{7})

2 a = \frac{4}{7} : a = \frac{2}{7}

Addiere und subtrahiere

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

7 (x^{2} + \frac{4 x}{7} + (\frac{2}{7})^{2} - (\frac{2}{7})^{2})

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

x^{2} + \frac{4}{7} x + (\frac{2}{7})^{2} = (x + \frac{2}{7})^{2}

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

Vereinfache

7 (x + \frac{2}{7})^{2} - \frac{4}{7}

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

so l v e f or x, (x - 6)^{2} + (y - 8)^{2} = k

so l v e f or x, x^{2} - y^{2} + 2 x y = 0

(a + 2) (2 a + 4) (2) = 5 (4) (2) + 156

3 x^{2} - 2 = 25