completesquare 49x^2-7x-3/4

Lösung

vervollständige das quadrat

49 x^{2} - 7 x - \frac{3}{4}

49 (x - \frac{1}{14})^{2} - 1

Schritte zur Lösung

49 x^{2} - 7 x - \frac{3}{4}

Schreibe

49 x^{2} - 7 x - \frac{3}{4}

in dieser Form:

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

Klammere aus

49

49 (x^{2} - \frac{x}{7} - \frac{3}{196})

2 a = - \frac{1}{7} : a = - \frac{1}{14}

Addiere und subtrahiere

(- \frac{1}{14})^{2}

49 (x^{2} - \frac{x}{7} - \frac{3}{196} + (- \frac{1}{14})^{2} - (- \frac{1}{14})^{2})

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

x^{2} - \frac{1}{7} x + (- \frac{1}{14})^{2} = (x - \frac{1}{14})^{2}

49 ((x - \frac{1}{14})^{2} - \frac{3}{196} - (- \frac{1}{14})^{2})

Vereinfache

49 (x - \frac{1}{14})^{2} - 1

5 x^{2} + 3 x + 7 = 0

- t^{2} + 78 t + 460 = 1581

12 x^{2} + 24 = - 40

x^{2} = - x + 12

(x^{2} - x - 3) lo g_{10} (4) = 3 lo g_{10} (\frac{1}{4})