completesquare 3+4x-4x^2

Lösung

vervollständige das quadrat

3 + 4 x - 4 x^{2}

- 4 (x - \frac{1}{2})^{2} + 4

Schritte zur Lösung

3 + 4 x - 4 x^{2}

Schreibe in der Standard Form

a x^{2} + b x + c

- 4 x^{2} + 4 x + 3

Schreibe

- 4 x^{2} + 4 x + 3

in dieser Form:

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

Klammere aus

- 4

- 4 (x^{2} - x - \frac{3}{4})

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

Addiere und subtrahiere

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

- 4 (x^{2} - x - \frac{3}{4} + (- \frac{1}{2})^{2} - (- \frac{1}{2})^{2})

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

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

- 4 ((x - \frac{1}{2})^{2} - \frac{3}{4} - (- \frac{1}{2})^{2})

Vereinfache

- 4 (x - \frac{1}{2})^{2} + 4

(4 x - 3)^{2} = 9

(3 x + 1)^{2} - (3 x - 1)^{2} - 5 (2 x - 1) = (x + 1)^{2}

4 = c^{2}

m^{2} - 12 m + 36 = 0

6 k^{2} - 14 k + 56 = 7 + 5 k^{2}