completesquare 10x^2-3x+1

Lösung

vervollständige das quadrat

10 x^{2} - 3 x + 1

10 (x - \frac{3}{20})^{2} + \frac{31}{40}

Schritte zur Lösung

10 x^{2} - 3 x + 1

Schreibe

10 x^{2} - 3 x + 1

in dieser Form:

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

Klammere aus

10

10 (x^{2} - \frac{3 x}{10} + \frac{1}{10})

2 a = - \frac{3}{10} : a = - \frac{3}{20}

Addiere und subtrahiere

(- \frac{3}{20})^{2}

10 (x^{2} - \frac{3 x}{10} + \frac{1}{10} + (- \frac{3}{20})^{2} - (- \frac{3}{20})^{2})

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

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

10 ((x - \frac{3}{20})^{2} + \frac{1}{10} - (- \frac{3}{20})^{2})

Vereinfache

10 (x - \frac{3}{20})^{2} + \frac{31}{40}

(2 x + 7)^{2} = 48

2 x^{2} - 15 x - 27 = 0

so l v e f or x, y = 5 x - x^{2}

so l v e f or x, x^{2} + 9 x + 20 = 0

9 x^{2} = 2 x