Whakaoti i te 6t+35t^2/2=12

$$6t+ \frac{ 35 { t }^{ 2 } }{ 2 } = 12$$

Whakaoti mō t

$$t=\frac{2\sqrt{219}-6}{35}\approx 0.674208491$$

$$t=\frac{-2\sqrt{219}-6}{35}\approx -1.017065634$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$12t+35t^{2}=24$$

Tangohia te 24 mai i ngā taha e rua.

$$12t+35t^{2}-24=0$$

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.

$$35t^{2}+12t-24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 35 mō a, 12 mō b, me -24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-12±\sqrt{12^{2}-4\times 35\left(-24\right)}}{2\times 35}$$

Pūrua 12.

$$t=\frac{-12±\sqrt{144-4\times 35\left(-24\right)}}{2\times 35}$$

Whakareatia -4 ki te 35.

$$t=\frac{-12±\sqrt{144-140\left(-24\right)}}{2\times 35}$$

Whakareatia -140 ki te -24.

$$t=\frac{-12±\sqrt{144+3360}}{2\times 35}$$

Tāpiri 144 ki te 3360.

$$t=\frac{-12±\sqrt{3504}}{2\times 35}$$

Tuhia te pūtakerua o te 3504.

$$t=\frac{-12±4\sqrt{219}}{2\times 35}$$

Whakareatia 2 ki te 35.

$$t=\frac{-12±4\sqrt{219}}{70}$$

Nā, me whakaoti te whārite t=\frac{-12±4\sqrt{219}}{70} ina he tāpiri te ±. Tāpiri -12 ki te 4\sqrt{219}.

$$t=\frac{4\sqrt{219}-12}{70}$$

Whakawehe -12+4\sqrt{219} ki te 70.

$$t=\frac{2\sqrt{219}-6}{35}$$

Nā, me whakaoti te whārite t=\frac{-12±4\sqrt{219}}{70} ina he tango te ±. Tango 4\sqrt{219} mai i -12.

$$t=\frac{-4\sqrt{219}-12}{70}$$

Whakawehe -12-4\sqrt{219} ki te 70.

$$t=\frac{-2\sqrt{219}-6}{35}$$

Kua oti te whārite te whakatau.

$$t=\frac{2\sqrt{219}-6}{35} t=\frac{-2\sqrt{219}-6}{35}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$12t+35t^{2}=24$$

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.

$$35t^{2}+12t=24$$

Whakawehea ngā taha e rua ki te 35.

$$\frac{35t^{2}+12t}{35}=\frac{24}{35}$$

Mā te whakawehe ki te 35 ka wetekia te whakareanga ki te 35.

$$t^{2}+\frac{12}{35}t=\frac{24}{35}$$

Whakawehea te \frac{12}{35}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{6}{35}. Nā, tāpiria te pūrua o te \frac{6}{35} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}+\frac{12}{35}t+\left(\frac{6}{35}\right)^{2}=\frac{24}{35}+\left(\frac{6}{35}\right)^{2}$$

Pūruatia \frac{6}{35} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}+\frac{12}{35}t+\frac{36}{1225}=\frac{24}{35}+\frac{36}{1225}$$

Tāpiri \frac{24}{35} ki te \frac{36}{1225} 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.

$$t^{2}+\frac{12}{35}t+\frac{36}{1225}=\frac{876}{1225}$$

Tauwehea t^{2}+\frac{12}{35}t+\frac{36}{1225}. 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}.

$$\left(t+\frac{6}{35}\right)^{2}=\frac{876}{1225}$$

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

$$\sqrt{\left(t+\frac{6}{35}\right)^{2}}=\sqrt{\frac{876}{1225}}$$

Whakarūnātia.

$$t+\frac{6}{35}=\frac{2\sqrt{219}}{35} t+\frac{6}{35}=-\frac{2\sqrt{219}}{35}$$

Me tango \frac{6}{35} mai i ngā taha e rua o te whārite.

$$t=\frac{2\sqrt{219}-6}{35} t=\frac{-2\sqrt{219}-6}{35}$$