completesquare-1/10 (x+10)(x-20)

Lösung

vervollständige das quadrat

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

- \frac{1}{10} (x - 5)^{2} + \frac{45}{2}

Schritte zur Lösung

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

Schreibe in der Standard Form

a x^{2} + b x + c

- \frac{x ^{2}}{10} + x + 20

Schreibe

- \frac{x ^{2}}{10} + x + 20

in dieser Form:

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

Klammere aus

- \frac{1}{10}

- \frac{1}{10} (x^{2} - 10 x - 200)

2 a = - 10 : a = - 5

Addiere und subtrahiere

(- 5)^{2}

- \frac{1}{10} (x^{2} - 10 x - 200 + (- 5)^{2} - (- 5)^{2})

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

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

- \frac{1}{10} ((x - 5)^{2} - 200 - (- 5)^{2})

Vereinfache

- \frac{1}{10} (x - 5)^{2} + \frac{45}{2}

7 x^{2} + 4 \cdot (- 3) = 0

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

so l v e f or y, y^{2} - 8 y + 16 = 0

7 d^{2} + 8 d - 3 = 0

x^{2} + 2 x \cdot 9 = 2 x + 2 \cdot 40