completesquare 10x^2-2x-1

Lösung

vervollständige das quadrat

10 x^{2} - 2 x - 1

10 (x - \frac{1}{10})^{2} - \frac{11}{10}

Schritte zur Lösung

10 x^{2} - 2 x - 1

Schreibe

10 x^{2} - 2 x - 1

in dieser Form:

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

Klammere aus

10

10 (x^{2} - \frac{x}{5} - \frac{1}{10})

2 a = - \frac{1}{5} : a = - \frac{1}{10}

Addiere und subtrahiere

(- \frac{1}{10})^{2}

10 (x^{2} - \frac{x}{5} - \frac{1}{10} + (- \frac{1}{10})^{2} - (- \frac{1}{10})^{2})

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

x^{2} - \frac{1}{5} x + (- \frac{1}{10})^{2} = (x - \frac{1}{10})^{2}

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

Vereinfache

10 (x - \frac{1}{10})^{2} - \frac{11}{10}

x^{2} + 3 x - 25 = 0

x^{2} = - 11 x + 80

- 3 x^{2} - 9 x + 357 = 9 x

so l v e f or x, z = 9 - 2 x^{2} - 2 y^{2}

y^{2} + 4 y - 2 = 0