Whakaoti i te t^2-107t+900=0

$$t ^ { 2 } - 107 t + 900 = 0$$

Whakaoti mō t

$$t = \frac{\sqrt{7849} + 107}{2} \approx 97.797291114$$

$$t = \frac{107 - \sqrt{7849}}{2} \approx 9.202708886$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$t^{2}-107t+900=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -107 mō b, me 900 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-107\right)±\sqrt{\left(-107\right)^{2}-4\times 900}}{2}$$

Pūrua -107.

$$t=\frac{-\left(-107\right)±\sqrt{11449-4\times 900}}{2}$$

Whakareatia -4 ki te 900.

$$t=\frac{-\left(-107\right)±\sqrt{11449-3600}}{2}$$

Tāpiri 11449 ki te -3600.

$$t=\frac{-\left(-107\right)±\sqrt{7849}}{2}$$

Ko te tauaro o -107 ko 107.

$$t=\frac{107±\sqrt{7849}}{2}$$

Nā, me whakaoti te whārite t=\frac{107±\sqrt{7849}}{2} ina he tāpiri te ±. Tāpiri 107 ki te \sqrt{7849}.

$$t=\frac{\sqrt{7849}+107}{2}$$

Nā, me whakaoti te whārite t=\frac{107±\sqrt{7849}}{2} ina he tango te ±. Tango \sqrt{7849} mai i 107.

$$t=\frac{107-\sqrt{7849}}{2}$$

Kua oti te whārite te whakatau.

$$t=\frac{\sqrt{7849}+107}{2} t=\frac{107-\sqrt{7849}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$t^{2}-107t+900=0$$

Me tango 900 mai i ngā taha e rua o te whārite.

$$t^{2}-107t+900-900=-900$$

Mā te tango i te 900 i a ia ake anō ka toe ko te 0.

$$t^{2}-107t=-900$$

Whakawehea te -107, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{107}{2}. Nā, tāpiria te pūrua o te -\frac{107}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-107t+\left(-\frac{107}{2}\right)^{2}=-900+\left(-\frac{107}{2}\right)^{2}$$

Pūruatia -\frac{107}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-107t+\frac{11449}{4}=-900+\frac{11449}{4}$$

Tāpiri -900 ki te \frac{11449}{4}.

$$t^{2}-107t+\frac{11449}{4}=\frac{7849}{4}$$

Tauwehea te t^{2}-107t+\frac{11449}{4}. 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}.

$$\left(t-\frac{107}{2}\right)^{2}=\frac{7849}{4}$$

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

$$\sqrt{\left(t-\frac{107}{2}\right)^{2}}=\sqrt{\frac{7849}{4}}$$

Whakarūnātia.

$$t-\frac{107}{2}=\frac{\sqrt{7849}}{2} t-\frac{107}{2}=-\frac{\sqrt{7849}}{2}$$

Me tāpiri \frac{107}{2} ki ngā taha e rua o te whārite.

$$t=\frac{\sqrt{7849}+107}{2} t=\frac{107-\sqrt{7849}}{2}$$