completesquare-4.9t^2+12.25t+115

Lösung

vervollständige das quadrat

- 4.9 t^{2} + 12.25 t + 115

- 4.9 (t - 1.25)^{2} + 122.65625

Schritte zur Lösung

- 4.9 t^{2} + 12.25 t + 115

Schreibe

- 4.9 t^{2} + 12.25 t + 115

in dieser Form:

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

Klammere aus

- 4.9

- 4.9 (t^{2} - \frac{12.25 t}{4.9} - \frac{115}{4.9})

2 a = - \frac{12.25}{4.9} : a = - 1.25

Addiere und subtrahiere

(- 1.25)^{2}

- 4.9 (t^{2} - \frac{12.25 t}{4.9} - \frac{115}{4.9} + (- 1.25)^{2} - (- 1.25)^{2})

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

t^{2} - \frac{12.25}{4.9} t + (- 1.25)^{2} = (t - 1.25)^{2}

- 4.9 ((t - 1.25)^{2} - \frac{115}{4.9} - (- 1.25)^{2})

Vereinfache

- 4.9 (t - 1.25)^{2} + 122.65625

x^{2} + 8 = - 17

so l v e f or x, x^{2} + 0^{2} - 4 = 0

roo t s 1 - x - x^{2}

roo t s 2 m^{2} - 5 m - 3

0 = x^{2} - 3 x - 9