Whakaoti i te 0=-5t^2+40t

$$0 = - 5 t ^ { 2 } + 40 t$$

Whakaoti mō t

$$t=8$$

$$t=0$$

Ngā Upane Whakamahi Tauwehe

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-5t^{2}+40t=0$$

Tauwehea te t.

$$t\left(-5t+40\right)=0$$

Hei kimi otinga whārite, me whakaoti te t=0 me te -5t+40=0.

$$t=0 t=8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-5t^{2}+40t=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 40 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-40±\sqrt{40^{2}}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 40^{2}.

$$t=\frac{-40±40}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$t=\frac{-40±40}{-10}$$

Nā, me whakaoti te whārite t=\frac{-40±40}{-10} ina he tāpiri te ±. Tāpiri -40 ki te 40.

$$t=\frac{0}{-10}$$

Whakawehe 0 ki te -10.

$$t=0$$

Nā, me whakaoti te whārite t=\frac{-40±40}{-10} ina he tango te ±. Tango 40 mai i -40.

$$t=-\frac{80}{-10}$$

Whakawehe -80 ki te -10.

$$t=8$$

Kua oti te whārite te whakatau.

$$t=0 t=8$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-5t^{2}+40t=0$$

Whakawehea ngā taha e rua ki te -5.

$$\frac{-5t^{2}+40t}{-5}=\frac{0}{-5}$$

Mā te whakawehe ki te -5 ka wetekia te whakareanga ki te -5.

$$t^{2}+\frac{40}{-5}t=\frac{0}{-5}$$

Whakawehe 40 ki te -5.

$$t^{2}-8t=\frac{0}{-5}$$

Whakawehe 0 ki te -5.

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

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

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

Pūrua -4.

$$t^{2}-8t+16=16$$

Tauwehea t^{2}-8t+16. 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}.

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

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

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

Whakarūnātia.

$$t-4=4 t-4=-4$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$t=8 t=0$$