Whakaoti i te 10t-14t^2=0

$$10 t - 14 t ^ { 2 } = 0$$

Whakaoti mō t

$$t=\frac{5}{7}\approx 0.714285714$$

$$t=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te t.

$$t\left(10-14t\right)=0$$

Hei kimi otinga whārite, me whakaoti te t=0 me te 10-14t=0.

$$t=0 t=\frac{5}{7}$$

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.

$$-14t^{2}+10t=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -14 mō a, 10 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-10±\sqrt{10^{2}}}{2\left(-14\right)}$$

Tuhia te pūtakerua o te 10^{2}.

$$t=\frac{-10±10}{2\left(-14\right)}$$

Whakareatia 2 ki te -14.

$$t=\frac{-10±10}{-28}$$

Nā, me whakaoti te whārite t=\frac{-10±10}{-28} ina he tāpiri te ±. Tāpiri -10 ki te 10.

$$t=\frac{0}{-28}$$

Whakawehe 0 ki te -28.

$$t=0$$

Nā, me whakaoti te whārite t=\frac{-10±10}{-28} ina he tango te ±. Tango 10 mai i -10.

$$t=-\frac{20}{-28}$$

Whakahekea te hautanga \frac{-20}{-28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$t=\frac{5}{7}$$

Kua oti te whārite te whakatau.

$$t=0 t=\frac{5}{7}$$

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.

$$-14t^{2}+10t=0$$

Whakawehea ngā taha e rua ki te -14.

$$\frac{-14t^{2}+10t}{-14}=\frac{0}{-14}$$

Mā te whakawehe ki te -14 ka wetekia te whakareanga ki te -14.

$$t^{2}+\frac{10}{-14}t=\frac{0}{-14}$$

Whakahekea te hautanga \frac{10}{-14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$t^{2}-\frac{5}{7}t=\frac{0}{-14}$$

Whakawehe 0 ki te -14.

$$t^{2}-\frac{5}{7}t=0$$

Whakawehea te -\frac{5}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{14}. Nā, tāpiria te pūrua o te -\frac{5}{14} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{5}{7}t+\left(-\frac{5}{14}\right)^{2}=\left(-\frac{5}{14}\right)^{2}$$

Pūruatia -\frac{5}{14} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{5}{7}t+\frac{25}{196}=\frac{25}{196}$$

Tauwehea t^{2}-\frac{5}{7}t+\frac{25}{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}.

$$\left(t-\frac{5}{14}\right)^{2}=\frac{25}{196}$$

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

$$\sqrt{\left(t-\frac{5}{14}\right)^{2}}=\sqrt{\frac{25}{196}}$$

Whakarūnātia.

$$t-\frac{5}{14}=\frac{5}{14} t-\frac{5}{14}=-\frac{5}{14}$$

Me tāpiri \frac{5}{14} ki ngā taha e rua o te whārite.

$$t=\frac{5}{7} t=0$$