Whakaoti i te 0.6t-160/3*5*10^-4/4*10^-3t^2=-2.04

$$0.6 t - \frac { \frac { 160 } { 3 } \times 5 \times 10 ^ { - 4 } } { 4 \times 10 ^ { - 3 } } t ^ { 2 } = - 2.04$$

Whakaoti mō t

$$t=-0.51$$

$$t=0.6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te taurunga i te taupū o te tauraro.

$$0.6t-\frac{5\times \frac{160}{3}}{4\times 10^{1}}t^{2}=-2.04$$

Whakareatia te 5 ki te \frac{160}{3}, ka \frac{800}{3}.

$$0.6t-\frac{\frac{800}{3}}{4\times 10^{1}}t^{2}=-2.04$$

Tātaihia te 10 mā te pū o 1, kia riro ko 10.

$$0.6t-\frac{\frac{800}{3}}{4\times 10}t^{2}=-2.04$$

Whakareatia te 4 ki te 10, ka 40.

$$0.6t-\frac{\frac{800}{3}}{40}t^{2}=-2.04$$

Tuhia te \frac{\frac{800}{3}}{40} hei hautanga kotahi.

$$0.6t-\frac{800}{3\times 40}t^{2}=-2.04$$

Whakareatia te 3 ki te 40, ka 120.

$$0.6t-\frac{800}{120}t^{2}=-2.04$$

Whakahekea te hautanga \frac{800}{120} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$0.6t-\frac{20}{3}t^{2}=-2.04$$

Me tāpiri te 2.04 ki ngā taha e rua.

$$0.6t-\frac{20}{3}t^{2}+2.04=0$$

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.

$$-\frac{20}{3}t^{2}+\frac{3}{5}t+2.04=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -\frac{20}{3} mō a, \frac{3}{5} mō b, me 2.04 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\frac{3}{5}±\sqrt{\left(\frac{3}{5}\right)^{2}-4\left(-\frac{20}{3}\right)\times 2.04}}{2\left(-\frac{20}{3}\right)}$$

Pūruatia \frac{3}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t=\frac{-\frac{3}{5}±\sqrt{\frac{9}{25}-4\left(-\frac{20}{3}\right)\times 2.04}}{2\left(-\frac{20}{3}\right)}$$

Whakareatia -4 ki te -\frac{20}{3}.

$$t=\frac{-\frac{3}{5}±\sqrt{\frac{9}{25}+\frac{80}{3}\times 2.04}}{2\left(-\frac{20}{3}\right)}$$

Whakareatia \frac{80}{3} ki te 2.04 mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$t=\frac{-\frac{3}{5}±\sqrt{\frac{9}{25}+\frac{272}{5}}}{2\left(-\frac{20}{3}\right)}$$

Tāpiri \frac{9}{25} ki te \frac{272}{5} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$t=\frac{-\frac{3}{5}±\sqrt{\frac{1369}{25}}}{2\left(-\frac{20}{3}\right)}$$

Tuhia te pūtakerua o te \frac{1369}{25}.

$$t=\frac{-\frac{3}{5}±\frac{37}{5}}{2\left(-\frac{20}{3}\right)}$$

Whakareatia 2 ki te -\frac{20}{3}.

$$t=\frac{-\frac{3}{5}±\frac{37}{5}}{-\frac{40}{3}}$$

Nā, me whakaoti te whārite t=\frac{-\frac{3}{5}±\frac{37}{5}}{-\frac{40}{3}} ina he tāpiri te ±. Tāpiri -\frac{3}{5} ki te \frac{37}{5} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$t=\frac{\frac{34}{5}}{-\frac{40}{3}}$$

Whakawehe \frac{34}{5} ki te -\frac{40}{3} mā te whakarea \frac{34}{5} ki te tau huripoki o -\frac{40}{3}.

$$t=-\frac{51}{100}$$

Nā, me whakaoti te whārite t=\frac{-\frac{3}{5}±\frac{37}{5}}{-\frac{40}{3}} ina he tango te ±. Tango \frac{37}{5} mai i -\frac{3}{5} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$t=-\frac{8}{-\frac{40}{3}}$$

Whakawehe -8 ki te -\frac{40}{3} mā te whakarea -8 ki te tau huripoki o -\frac{40}{3}.

$$t=\frac{3}{5}$$

Kua oti te whārite te whakatau.

$$t=-\frac{51}{100} t=\frac{3}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te taurunga i te taupū o te tauraro.

$$0.6t-\frac{5\times \frac{160}{3}}{4\times 10^{1}}t^{2}=-2.04$$

Whakareatia te 5 ki te \frac{160}{3}, ka \frac{800}{3}.

$$0.6t-\frac{\frac{800}{3}}{4\times 10^{1}}t^{2}=-2.04$$

Tātaihia te 10 mā te pū o 1, kia riro ko 10.

$$0.6t-\frac{\frac{800}{3}}{4\times 10}t^{2}=-2.04$$

Whakareatia te 4 ki te 10, ka 40.

$$0.6t-\frac{\frac{800}{3}}{40}t^{2}=-2.04$$

Tuhia te \frac{\frac{800}{3}}{40} hei hautanga kotahi.

$$0.6t-\frac{800}{3\times 40}t^{2}=-2.04$$

Whakareatia te 3 ki te 40, ka 120.

$$0.6t-\frac{800}{120}t^{2}=-2.04$$

Whakahekea te hautanga \frac{800}{120} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$0.6t-\frac{20}{3}t^{2}=-2.04$$

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.

$$-\frac{20}{3}t^{2}+\frac{3}{5}t=-2.04$$

Whakawehea ngā taha e rua o te whārite ki te -\frac{20}{3}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-\frac{20}{3}t^{2}+\frac{3}{5}t}{-\frac{20}{3}}=-\frac{2.04}{-\frac{20}{3}}$$

Mā te whakawehe ki te -\frac{20}{3} ka wetekia te whakareanga ki te -\frac{20}{3}.

$$t^{2}+\frac{\frac{3}{5}}{-\frac{20}{3}}t=-\frac{2.04}{-\frac{20}{3}}$$

Whakawehe \frac{3}{5} ki te -\frac{20}{3} mā te whakarea \frac{3}{5} ki te tau huripoki o -\frac{20}{3}.

$$t^{2}-\frac{9}{100}t=-\frac{2.04}{-\frac{20}{3}}$$

Whakawehe -2.04 ki te -\frac{20}{3} mā te whakarea -2.04 ki te tau huripoki o -\frac{20}{3}.

$$t^{2}-\frac{9}{100}t=\frac{153}{500}$$

Whakawehea te -\frac{9}{100}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{200}. Nā, tāpiria te pūrua o te -\frac{9}{200} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{9}{100}t+\left(-\frac{9}{200}\right)^{2}=\frac{153}{500}+\left(-\frac{9}{200}\right)^{2}$$

Pūruatia -\frac{9}{200} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{9}{100}t+\frac{81}{40000}=\frac{153}{500}+\frac{81}{40000}$$

Tāpiri \frac{153}{500} ki te \frac{81}{40000} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$t^{2}-\frac{9}{100}t+\frac{81}{40000}=\frac{12321}{40000}$$

Tauwehea t^{2}-\frac{9}{100}t+\frac{81}{40000}. 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}.

$$\left(t-\frac{9}{200}\right)^{2}=\frac{12321}{40000}$$

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

$$\sqrt{\left(t-\frac{9}{200}\right)^{2}}=\sqrt{\frac{12321}{40000}}$$

Whakarūnātia.

$$t-\frac{9}{200}=\frac{111}{200} t-\frac{9}{200}=-\frac{111}{200}$$

Me tāpiri \frac{9}{200} ki ngā taha e rua o te whārite.

$$t=\frac{3}{5} t=-\frac{51}{100}$$