Whakaoti i te 5t^2/2t=4/5

$$\frac { 5 t ^ { 2 } } { 2 t } = \frac { 4 } { 5 }$$

Whakaoti mō t

$$t=\frac{8}{25}=0.32$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe t ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10t, arā, te tauraro pātahi he tino iti rawa te kitea o 2t,5.

$$5\times 5t^{2}=8t$$

Whakareatia te 5 ki te 5, ka 25.

$$25t^{2}=8t$$

Tangohia te 8t mai i ngā taha e rua.

$$25t^{2}-8t=0$$

Tauwehea te t.

$$t\left(25t-8\right)=0$$

Hei kimi otinga whārite, me whakaoti te t=0 me te 25t-8=0.

$$t=0 t=\frac{8}{25}$$

Tē taea kia ōrite te tāupe t ki 0.

$$t=\frac{8}{25}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe t ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10t, arā, te tauraro pātahi he tino iti rawa te kitea o 2t,5.

$$5\times 5t^{2}=8t$$

Whakareatia te 5 ki te 5, ka 25.

$$25t^{2}=8t$$

Tangohia te 8t mai i ngā taha e rua.

$$25t^{2}-8t=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 25 mō a, -8 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2\times 25}$$

Tuhia te pūtakerua o te \left(-8\right)^{2}.

$$t=\frac{-\left(-8\right)±8}{2\times 25}$$

Ko te tauaro o -8 ko 8.

$$t=\frac{8±8}{2\times 25}$$

Whakareatia 2 ki te 25.

$$t=\frac{8±8}{50}$$

Nā, me whakaoti te whārite t=\frac{8±8}{50} ina he tāpiri te ±. Tāpiri 8 ki te 8.

$$t=\frac{16}{50}$$

Whakahekea te hautanga \frac{16}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$t=\frac{8}{25}$$

Nā, me whakaoti te whārite t=\frac{8±8}{50} ina he tango te ±. Tango 8 mai i 8.

$$t=\frac{0}{50}$$

Whakawehe 0 ki te 50.

$$t=0$$

Kua oti te whārite te whakatau.

$$t=\frac{8}{25} t=0$$

Tē taea kia ōrite te tāupe t ki 0.

$$t=\frac{8}{25}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe t ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10t, arā, te tauraro pātahi he tino iti rawa te kitea o 2t,5.

$$5\times 5t^{2}=8t$$

Whakareatia te 5 ki te 5, ka 25.

$$25t^{2}=8t$$

Tangohia te 8t mai i ngā taha e rua.

$$25t^{2}-8t=0$$

Whakawehea ngā taha e rua ki te 25.

$$\frac{25t^{2}-8t}{25}=\frac{0}{25}$$

Mā te whakawehe ki te 25 ka wetekia te whakareanga ki te 25.

$$t^{2}-\frac{8}{25}t=\frac{0}{25}$$

Whakawehe 0 ki te 25.

$$t^{2}-\frac{8}{25}t=0$$

Whakawehea te -\frac{8}{25}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{4}{25}. Nā, tāpiria te pūrua o te -\frac{4}{25} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{8}{25}t+\left(-\frac{4}{25}\right)^{2}=\left(-\frac{4}{25}\right)^{2}$$

Pūruatia -\frac{4}{25} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{8}{25}t+\frac{16}{625}=\frac{16}{625}$$

Tauwehea t^{2}-\frac{8}{25}t+\frac{16}{625}. 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}.

$$\left(t-\frac{4}{25}\right)^{2}=\frac{16}{625}$$

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

$$\sqrt{\left(t-\frac{4}{25}\right)^{2}}=\sqrt{\frac{16}{625}}$$

Whakarūnātia.

$$t-\frac{4}{25}=\frac{4}{25} t-\frac{4}{25}=-\frac{4}{25}$$

Me tāpiri \frac{4}{25} ki ngā taha e rua o te whārite.

$$t=\frac{8}{25} t=0$$

Tē taea kia ōrite te tāupe t ki 0.

$$t=\frac{8}{25}$$