completesquare 25x^2+30x+12

Lösung

vervollständige das quadrat

25 x^{2} + 30 x + 12

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

Schritte zur Lösung

25 x^{2} + 30 x + 12

Schreibe

25 x^{2} + 30 x + 12

in dieser Form:

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

Klammere aus

25

25 (x^{2} + \frac{6 x}{5} + \frac{12}{25})

2 a = \frac{6}{5} : a = \frac{3}{5}

Addiere und subtrahiere

(\frac{3}{5})^{2}

25 (x^{2} + \frac{6 x}{5} + \frac{12}{25} + (\frac{3}{5})^{2} - (\frac{3}{5})^{2})

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

x^{2} + \frac{6}{5} x + (\frac{3}{5})^{2} = (x + \frac{3}{5})^{2}

25 ((x + \frac{3}{5})^{2} + \frac{12}{25} - (\frac{3}{5})^{2})

Vereinfache

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

so l v e f or t, h = v t - g t^{2}

x^{2} - 13 x + 1 = - 9 x + 6

co m pl e t es q u a re x^{2} + 3 x + 10

so l v e f or x, x^{2} = a x y + b y

2 x^{2} - 7 x - 8 = 12