Whakaoti i te 2t=-5+t^2

$$2 t = - 5 + t ^ { 2 }$$

Whakaoti mō t

$$t=\sqrt{6}+1\approx 3.449489743$$

$$t=1-\sqrt{6}\approx -1.449489743$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te -5 mai i ngā taha e rua.

$$2t-\left(-5\right)=t^{2}$$

Ko te tauaro o -5 ko 5.

$$2t+5=t^{2}$$

Tangohia te t^{2} mai i ngā taha e rua.

$$2t+5-t^{2}=0$$

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.

$$-t^{2}+2t+5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 2 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-2±\sqrt{2^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Pūrua 2.

$$t=\frac{-2±\sqrt{4-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$t=\frac{-2±\sqrt{4+4\times 5}}{2\left(-1\right)}$$

Whakareatia 4 ki te 5.

$$t=\frac{-2±\sqrt{4+20}}{2\left(-1\right)}$$

Tāpiri 4 ki te 20.

$$t=\frac{-2±\sqrt{24}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 24.

$$t=\frac{-2±2\sqrt{6}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$t=\frac{-2±2\sqrt{6}}{-2}$$

Nā, me whakaoti te whārite t=\frac{-2±2\sqrt{6}}{-2} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{6}.

$$t=\frac{2\sqrt{6}-2}{-2}$$

Whakawehe -2+2\sqrt{6} ki te -2.

$$t=1-\sqrt{6}$$

Nā, me whakaoti te whārite t=\frac{-2±2\sqrt{6}}{-2} ina he tango te ±. Tango 2\sqrt{6} mai i -2.

$$t=\frac{-2\sqrt{6}-2}{-2}$$

Whakawehe -2-2\sqrt{6} ki te -2.

$$t=\sqrt{6}+1$$

Kua oti te whārite te whakatau.

$$t=1-\sqrt{6} t=\sqrt{6}+1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te t^{2} mai i ngā taha e rua.

$$2t-t^{2}=-5$$

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.

$$-t^{2}+2t=-5$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-t^{2}+2t}{-1}=-\frac{5}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$t^{2}+\frac{2}{-1}t=-\frac{5}{-1}$$

Whakawehe 2 ki te -1.

$$t^{2}-2t=-\frac{5}{-1}$$

Whakawehe -5 ki te -1.

$$t^{2}-2t=5$$

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-2t+1=5+1$$

Tāpiri 5 ki te 1.

$$t^{2}-2t+1=6$$

Tauwehea t^{2}-2t+1. 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}.

$$\left(t-1\right)^{2}=6$$

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

$$\sqrt{\left(t-1\right)^{2}}=\sqrt{6}$$

Whakarūnātia.

$$t-1=\sqrt{6} t-1=-\sqrt{6}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$t=\sqrt{6}+1 t=1-\sqrt{6}$$