Whakaoti i te 44t^2-244t=0

$$44 t ^ { 2 } - 244 t = 0$$

Whakaoti mō t

$$t = \frac{61}{11} = 5\frac{6}{11} \approx 5.545454545$$

$$t=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te t.

$$t\left(44t-244\right)=0$$

Hei kimi otinga whārite, me whakaoti te t=0 me te 44t-244=0.

$$t=0 t=\frac{61}{11}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$44t^{2}-244t=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 44 mō a, -244 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-244\right)±\sqrt{\left(-244\right)^{2}}}{2\times 44}$$

Tuhia te pūtakerua o te \left(-244\right)^{2}.

$$t=\frac{-\left(-244\right)±244}{2\times 44}$$

Ko te tauaro o -244 ko 244.

$$t=\frac{244±244}{2\times 44}$$

Whakareatia 2 ki te 44.

$$t=\frac{244±244}{88}$$

Nā, me whakaoti te whārite t=\frac{244±244}{88} ina he tāpiri te ±. Tāpiri 244 ki te 244.

$$t=\frac{488}{88}$$

Whakahekea te hautanga \frac{488}{88} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$t=\frac{61}{11}$$

Nā, me whakaoti te whārite t=\frac{244±244}{88} ina he tango te ±. Tango 244 mai i 244.

$$t=\frac{0}{88}$$

Whakawehe 0 ki te 88.

$$t=0$$

Kua oti te whārite te whakatau.

$$t=\frac{61}{11} t=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$44t^{2}-244t=0$$

Whakawehea ngā taha e rua ki te 44.

$$\frac{44t^{2}-244t}{44}=\frac{0}{44}$$

Mā te whakawehe ki te 44 ka wetekia te whakareanga ki te 44.

$$t^{2}+\left(-\frac{244}{44}\right)t=\frac{0}{44}$$

Whakahekea te hautanga \frac{-244}{44} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$t^{2}-\frac{61}{11}t=\frac{0}{44}$$

Whakawehe 0 ki te 44.

$$t^{2}-\frac{61}{11}t=0$$

Whakawehea te -\frac{61}{11}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{61}{22}. Nā, tāpiria te pūrua o te -\frac{61}{22} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{61}{11}t+\left(-\frac{61}{22}\right)^{2}=\left(-\frac{61}{22}\right)^{2}$$

Pūruatia -\frac{61}{22} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{61}{11}t+\frac{3721}{484}=\frac{3721}{484}$$

Tauwehea t^{2}-\frac{61}{11}t+\frac{3721}{484}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-\frac{61}{22}\right)^{2}=\frac{3721}{484}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(t-\frac{61}{22}\right)^{2}}=\sqrt{\frac{3721}{484}}$$

Whakarūnātia.

$$t-\frac{61}{22}=\frac{61}{22} t-\frac{61}{22}=-\frac{61}{22}$$

Me tāpiri \frac{61}{22} ki ngā taha e rua o te whārite.

$$t=\frac{61}{11} t=0$$