Whakaoti i te 0=105t+49t^2

$$0 = 105 t + 49 t ^ { 2 }$$

Whakaoti mō t

$$t = -\frac{15}{7} = -2\frac{1}{7} \approx -2.142857143$$

$$t=0$$

Ngā Upane Whakamahi Tauwehe

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

$$105t+49t^{2}=0$$

Tauwehea te t.

$$t\left(105+49t\right)=0$$

Hei kimi otinga whārite, me whakaoti te t=0 me te 105+49t=0.

$$t=0 t=-\frac{15}{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$105t+49t^{2}=0$$

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.

$$49t^{2}+105t=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 49 mō a, 105 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-105±\sqrt{105^{2}}}{2\times 49}$$

Tuhia te pūtakerua o te 105^{2}.

$$t=\frac{-105±105}{2\times 49}$$

Whakareatia 2 ki te 49.

$$t=\frac{-105±105}{98}$$

Nā, me whakaoti te whārite t=\frac{-105±105}{98} ina he tāpiri te ±. Tāpiri -105 ki te 105.

$$t=\frac{0}{98}$$

Whakawehe 0 ki te 98.

$$t=0$$

Nā, me whakaoti te whārite t=\frac{-105±105}{98} ina he tango te ±. Tango 105 mai i -105.

$$t=-\frac{210}{98}$$

Whakahekea te hautanga \frac{-210}{98} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$t=-\frac{15}{7}$$

Kua oti te whārite te whakatau.

$$t=0 t=-\frac{15}{7}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$105t+49t^{2}=0$$

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.

$$49t^{2}+105t=0$$

Whakawehea ngā taha e rua ki te 49.

$$\frac{49t^{2}+105t}{49}=\frac{0}{49}$$

Mā te whakawehe ki te 49 ka wetekia te whakareanga ki te 49.

$$t^{2}+\frac{105}{49}t=\frac{0}{49}$$

Whakahekea te hautanga \frac{105}{49} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$t^{2}+\frac{15}{7}t=\frac{0}{49}$$

Whakawehe 0 ki te 49.

$$t^{2}+\frac{15}{7}t=0$$

Whakawehea te \frac{15}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{15}{14}. Nā, tāpiria te pūrua o te \frac{15}{14} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}+\frac{15}{7}t+\left(\frac{15}{14}\right)^{2}=\left(\frac{15}{14}\right)^{2}$$

Pūruatia \frac{15}{14} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}+\frac{15}{7}t+\frac{225}{196}=\frac{225}{196}$$

Tauwehea t^{2}+\frac{15}{7}t+\frac{225}{196}. 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}.

$$\left(t+\frac{15}{14}\right)^{2}=\frac{225}{196}$$

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

$$\sqrt{\left(t+\frac{15}{14}\right)^{2}}=\sqrt{\frac{225}{196}}$$

Whakarūnātia.

$$t+\frac{15}{14}=\frac{15}{14} t+\frac{15}{14}=-\frac{15}{14}$$

Me tango \frac{15}{14} mai i ngā taha e rua o te whārite.

$$t=0 t=-\frac{15}{7}$$