completesquare 2x^2-10x+3

Lösung

vervollständige das quadrat

2 x^{2} - 10 x + 3

2 (x - \frac{5}{2})^{2} - \frac{19}{2}

Schritte zur Lösung

2 x^{2} - 10 x + 3

Schreibe

2 x^{2} - 10 x + 3

in dieser Form:

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

Klammere aus

2

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

2 a = - 5 : a = - \frac{5}{2}

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

2 (x - \frac{5}{2})^{2} - \frac{19}{2}

x^{2} + (- \frac{1}{6})^{2} = 1^{2}

(X + 2) (X - 3) + 2 (3 X - 4) = 3 X + 1

x^{2} + (\frac{90}{2000}) x + (\frac{1500}{2000}) = 0

x^{2} + (x - 7)^{2} = 132

(x + 13)^{2} = - 4