Whakaoti i te -20387=1018t+t^2

$$- 20387 = 1018 t + t ^ { 2 }$$

Whakaoti mō t

$$t=\sqrt{238694}-509\approx -20.436800403$$

$$t=-\sqrt{238694}-509\approx -997.563199597$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$1018t+t^{2}=-20387$$

Me tāpiri te 20387 ki ngā taha e rua.

$$1018t+t^{2}+20387=0$$

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.

$$t^{2}+1018t+20387=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1018 mō b, me 20387 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-1018±\sqrt{1018^{2}-4\times 20387}}{2}$$

Pūrua 1018.

$$t=\frac{-1018±\sqrt{1036324-4\times 20387}}{2}$$

Whakareatia -4 ki te 20387.

$$t=\frac{-1018±\sqrt{1036324-81548}}{2}$$

Tāpiri 1036324 ki te -81548.

$$t=\frac{-1018±\sqrt{954776}}{2}$$

Tuhia te pūtakerua o te 954776.

$$t=\frac{-1018±2\sqrt{238694}}{2}$$

Nā, me whakaoti te whārite t=\frac{-1018±2\sqrt{238694}}{2} ina he tāpiri te ±. Tāpiri -1018 ki te 2\sqrt{238694}.

$$t=\frac{2\sqrt{238694}-1018}{2}$$

Whakawehe -1018+2\sqrt{238694} ki te 2.

$$t=\sqrt{238694}-509$$

Nā, me whakaoti te whārite t=\frac{-1018±2\sqrt{238694}}{2} ina he tango te ±. Tango 2\sqrt{238694} mai i -1018.

$$t=\frac{-2\sqrt{238694}-1018}{2}$$

Whakawehe -1018-2\sqrt{238694} ki te 2.

$$t=-\sqrt{238694}-509$$

Kua oti te whārite te whakatau.

$$t=\sqrt{238694}-509 t=-\sqrt{238694}-509$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$1018t+t^{2}=-20387$$

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.

$$t^{2}+1018t=-20387$$

Whakawehea te 1018, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 509. Nā, tāpiria te pūrua o te 509 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}+1018t+509^{2}=-20387+509^{2}$$

Pūrua 509.

$$t^{2}+1018t+259081=-20387+259081$$

Tāpiri -20387 ki te 259081.

$$t^{2}+1018t+259081=238694$$

Tauwehea t^{2}+1018t+259081. 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}.

$$\left(t+509\right)^{2}=238694$$

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

$$\sqrt{\left(t+509\right)^{2}}=\sqrt{238694}$$

Whakarūnātia.

$$t+509=\sqrt{238694} t+509=-\sqrt{238694}$$

Me tango 509 mai i ngā taha e rua o te whārite.

$$t=\sqrt{238694}-509 t=-\sqrt{238694}-509$$