Whakaoti i te 301+2t^2=300t

$$301 + 2 t ^ { 2 } = 300 t$$

Whakaoti mō t

$$t=\frac{\sqrt{21898}}{2}+75\approx 148.989864171$$

$$t=-\frac{\sqrt{21898}}{2}+75\approx 1.010135829$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 300t mai i ngā taha e rua.

$$301+2t^{2}-300t=0$$

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.

$$2t^{2}-300t+301=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -300 mō b, me 301 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-300\right)±\sqrt{\left(-300\right)^{2}-4\times 2\times 301}}{2\times 2}$$

Pūrua -300.

$$t=\frac{-\left(-300\right)±\sqrt{90000-4\times 2\times 301}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$t=\frac{-\left(-300\right)±\sqrt{90000-8\times 301}}{2\times 2}$$

Whakareatia -8 ki te 301.

$$t=\frac{-\left(-300\right)±\sqrt{90000-2408}}{2\times 2}$$

Tāpiri 90000 ki te -2408.

$$t=\frac{-\left(-300\right)±\sqrt{87592}}{2\times 2}$$

Tuhia te pūtakerua o te 87592.

$$t=\frac{-\left(-300\right)±2\sqrt{21898}}{2\times 2}$$

Ko te tauaro o -300 ko 300.

$$t=\frac{300±2\sqrt{21898}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$t=\frac{300±2\sqrt{21898}}{4}$$

Nā, me whakaoti te whārite t=\frac{300±2\sqrt{21898}}{4} ina he tāpiri te ±. Tāpiri 300 ki te 2\sqrt{21898}.

$$t=\frac{2\sqrt{21898}+300}{4}$$

Whakawehe 300+2\sqrt{21898} ki te 4.

$$t=\frac{\sqrt{21898}}{2}+75$$

Nā, me whakaoti te whārite t=\frac{300±2\sqrt{21898}}{4} ina he tango te ±. Tango 2\sqrt{21898} mai i 300.

$$t=\frac{300-2\sqrt{21898}}{4}$$

Whakawehe 300-2\sqrt{21898} ki te 4.

$$t=-\frac{\sqrt{21898}}{2}+75$$

Kua oti te whārite te whakatau.

$$t=\frac{\sqrt{21898}}{2}+75 t=-\frac{\sqrt{21898}}{2}+75$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 300t mai i ngā taha e rua.

$$301+2t^{2}-300t=0$$

Tangohia te 301 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2t^{2}-300t=-301$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2t^{2}-300t}{2}=-\frac{301}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$t^{2}+\left(-\frac{300}{2}\right)t=-\frac{301}{2}$$

Whakawehe -300 ki te 2.

$$t^{2}-150t=-\frac{301}{2}$$

Whakawehea te -150, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -75. Nā, tāpiria te pūrua o te -75 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-150t+\left(-75\right)^{2}=-\frac{301}{2}+\left(-75\right)^{2}$$

Pūrua -75.

$$t^{2}-150t+5625=-\frac{301}{2}+5625$$

Tāpiri -\frac{301}{2} ki te 5625.

$$t^{2}-150t+5625=\frac{10949}{2}$$

Tauwehea te t^{2}-150t+5625. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-75\right)^{2}=\frac{10949}{2}$$

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

$$\sqrt{\left(t-75\right)^{2}}=\sqrt{\frac{10949}{2}}$$

Whakarūnātia.

$$t-75=\frac{\sqrt{21898}}{2} t-75=-\frac{\sqrt{21898}}{2}$$

Me tāpiri 75 ki ngā taha e rua o te whārite.

$$t=\frac{\sqrt{21898}}{2}+75 t=-\frac{\sqrt{21898}}{2}+75$$