Whakaoti i te 11(1)=-10t^2+44t+30

$$11 ( 1 ) = - 10 t ^ { 2 } + 44 t + 30$$

Whakaoti mō t

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5}\approx 4.796150997$$

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5}\approx -0.396150997$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 11 ki te 1, ka 11.

$$11=-10t^{2}+44t+30$$

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

$$-10t^{2}+44t+30=11$$

Tangohia te 11 mai i ngā taha e rua.

$$-10t^{2}+44t+30-11=0$$

Tangohia te 11 i te 30, ka 19.

$$-10t^{2}+44t+19=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -10 mō a, 44 mō b, me 19 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-44±\sqrt{44^{2}-4\left(-10\right)\times 19}}{2\left(-10\right)}$$

Pūrua 44.

$$t=\frac{-44±\sqrt{1936-4\left(-10\right)\times 19}}{2\left(-10\right)}$$

Whakareatia -4 ki te -10.

$$t=\frac{-44±\sqrt{1936+40\times 19}}{2\left(-10\right)}$$

Whakareatia 40 ki te 19.

$$t=\frac{-44±\sqrt{1936+760}}{2\left(-10\right)}$$

Tāpiri 1936 ki te 760.

$$t=\frac{-44±\sqrt{2696}}{2\left(-10\right)}$$

Tuhia te pūtakerua o te 2696.

$$t=\frac{-44±2\sqrt{674}}{2\left(-10\right)}$$

Whakareatia 2 ki te -10.

$$t=\frac{-44±2\sqrt{674}}{-20}$$

Nā, me whakaoti te whārite t=\frac{-44±2\sqrt{674}}{-20} ina he tāpiri te ±. Tāpiri -44 ki te 2\sqrt{674}.

$$t=\frac{2\sqrt{674}-44}{-20}$$

Whakawehe -44+2\sqrt{674} ki te -20.

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5}$$

Nā, me whakaoti te whārite t=\frac{-44±2\sqrt{674}}{-20} ina he tango te ±. Tango 2\sqrt{674} mai i -44.

$$t=\frac{-2\sqrt{674}-44}{-20}$$

Whakawehe -44-2\sqrt{674} ki te -20.

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5}$$

Kua oti te whārite te whakatau.

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5} t=\frac{\sqrt{674}}{10}+\frac{11}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 11 ki te 1, ka 11.

$$11=-10t^{2}+44t+30$$

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

$$-10t^{2}+44t+30=11$$

Tangohia te 30 mai i ngā taha e rua.

$$-10t^{2}+44t=11-30$$

Tangohia te 30 i te 11, ka -19.

$$-10t^{2}+44t=-19$$

Whakawehea ngā taha e rua ki te -10.

$$\frac{-10t^{2}+44t}{-10}=-\frac{19}{-10}$$

Mā te whakawehe ki te -10 ka wetekia te whakareanga ki te -10.

$$t^{2}+\frac{44}{-10}t=-\frac{19}{-10}$$

Whakahekea te hautanga \frac{44}{-10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$t^{2}-\frac{22}{5}t=-\frac{19}{-10}$$

Whakawehe -19 ki te -10.

$$t^{2}-\frac{22}{5}t=\frac{19}{10}$$

Whakawehea te -\frac{22}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{5}. Nā, tāpiria te pūrua o te -\frac{11}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{22}{5}t+\left(-\frac{11}{5}\right)^{2}=\frac{19}{10}+\left(-\frac{11}{5}\right)^{2}$$

Pūruatia -\frac{11}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{22}{5}t+\frac{121}{25}=\frac{19}{10}+\frac{121}{25}$$

Tāpiri \frac{19}{10} ki te \frac{121}{25} 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.

$$t^{2}-\frac{22}{5}t+\frac{121}{25}=\frac{337}{50}$$

Tauwehea t^{2}-\frac{22}{5}t+\frac{121}{25}. 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}.

$$\left(t-\frac{11}{5}\right)^{2}=\frac{337}{50}$$

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

$$\sqrt{\left(t-\frac{11}{5}\right)^{2}}=\sqrt{\frac{337}{50}}$$

Whakarūnātia.

$$t-\frac{11}{5}=\frac{\sqrt{674}}{10} t-\frac{11}{5}=-\frac{\sqrt{674}}{10}$$

Me tāpiri \frac{11}{5} ki ngā taha e rua o te whārite.

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5} t=-\frac{\sqrt{674}}{10}+\frac{11}{5}$$