Whakaoti i te -16t^2+80t+96=t

$$- 16 t ^ { 2 } + 80 t + 96 = t$$

Whakaoti mō t

$$t = \frac{\sqrt{12385} + 79}{32} \approx 5.94649734$$

$$t=\frac{79-\sqrt{12385}}{32}\approx -1.00899734$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te t mai i ngā taha e rua.

$$-16t^{2}+80t+96-t=0$$

Pahekotia te 80t me -t, ka 79t.

$$-16t^{2}+79t+96=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -16 mō a, 79 mō b, me 96 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-79±\sqrt{79^{2}-4\left(-16\right)\times 96}}{2\left(-16\right)}$$

Pūrua 79.

$$t=\frac{-79±\sqrt{6241-4\left(-16\right)\times 96}}{2\left(-16\right)}$$

Whakareatia -4 ki te -16.

$$t=\frac{-79±\sqrt{6241+64\times 96}}{2\left(-16\right)}$$

Whakareatia 64 ki te 96.

$$t=\frac{-79±\sqrt{6241+6144}}{2\left(-16\right)}$$

Tāpiri 6241 ki te 6144.

$$t=\frac{-79±\sqrt{12385}}{2\left(-16\right)}$$

Whakareatia 2 ki te -16.

$$t=\frac{-79±\sqrt{12385}}{-32}$$

Nā, me whakaoti te whārite t=\frac{-79±\sqrt{12385}}{-32} ina he tāpiri te ±. Tāpiri -79 ki te \sqrt{12385}.

$$t=\frac{\sqrt{12385}-79}{-32}$$

Whakawehe -79+\sqrt{12385} ki te -32.

$$t=\frac{79-\sqrt{12385}}{32}$$

Nā, me whakaoti te whārite t=\frac{-79±\sqrt{12385}}{-32} ina he tango te ±. Tango \sqrt{12385} mai i -79.

$$t=\frac{-\sqrt{12385}-79}{-32}$$

Whakawehe -79-\sqrt{12385} ki te -32.

$$t=\frac{\sqrt{12385}+79}{32}$$

Kua oti te whārite te whakatau.

$$t=\frac{79-\sqrt{12385}}{32} t=\frac{\sqrt{12385}+79}{32}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te t mai i ngā taha e rua.

$$-16t^{2}+80t+96-t=0$$

Pahekotia te 80t me -t, ka 79t.

$$-16t^{2}+79t+96=0$$

Tangohia te 96 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-16t^{2}+79t=-96$$

Whakawehea ngā taha e rua ki te -16.

$$\frac{-16t^{2}+79t}{-16}=-\frac{96}{-16}$$

Mā te whakawehe ki te -16 ka wetekia te whakareanga ki te -16.

$$t^{2}+\frac{79}{-16}t=-\frac{96}{-16}$$

Whakawehe 79 ki te -16.

$$t^{2}-\frac{79}{16}t=-\frac{96}{-16}$$

Whakawehe -96 ki te -16.

$$t^{2}-\frac{79}{16}t=6$$

Whakawehea te -\frac{79}{16}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{79}{32}. Nā, tāpiria te pūrua o te -\frac{79}{32} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{79}{16}t+\left(-\frac{79}{32}\right)^{2}=6+\left(-\frac{79}{32}\right)^{2}$$

Pūruatia -\frac{79}{32} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{79}{16}t+\frac{6241}{1024}=6+\frac{6241}{1024}$$

Tāpiri 6 ki te \frac{6241}{1024}.

$$t^{2}-\frac{79}{16}t+\frac{6241}{1024}=\frac{12385}{1024}$$

Tauwehea t^{2}-\frac{79}{16}t+\frac{6241}{1024}. 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}.

$$\left(t-\frac{79}{32}\right)^{2}=\frac{12385}{1024}$$

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

$$\sqrt{\left(t-\frac{79}{32}\right)^{2}}=\sqrt{\frac{12385}{1024}}$$

Whakarūnātia.

$$t-\frac{79}{32}=\frac{\sqrt{12385}}{32} t-\frac{79}{32}=-\frac{\sqrt{12385}}{32}$$

Me tāpiri \frac{79}{32} ki ngā taha e rua o te whārite.

$$t=\frac{\sqrt{12385}+79}{32} t=\frac{79-\sqrt{12385}}{32}$$