Whakaoti i te left(10-2tright)t=9.375

$$\left( 10-2t \right) t = 9.375$$

Whakaoti mō t

$$t=1.25$$

$$t=3.75$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 10-2t ki te t.

$$10t-2t^{2}=9.375$$

Tangohia te 9.375 mai i ngā taha e rua.

$$10t-2t^{2}-9.375=0$$

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.

$$-2t^{2}+10t-9.375=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 10 mō b, me -9.375 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-10±\sqrt{10^{2}-4\left(-2\right)\left(-9.375\right)}}{2\left(-2\right)}$$

Pūrua 10.

$$t=\frac{-10±\sqrt{100-4\left(-2\right)\left(-9.375\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$t=\frac{-10±\sqrt{100+8\left(-9.375\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -9.375.

$$t=\frac{-10±\sqrt{100-75}}{2\left(-2\right)}$$

Tāpiri 100 ki te -75.

$$t=\frac{-10±\sqrt{25}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 25.

$$t=\frac{-10±5}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$t=\frac{-10±5}{-4}$$

Nā, me whakaoti te whārite t=\frac{-10±5}{-4} ina he tāpiri te ±. Tāpiri -10 ki te 5.

$$t=-\frac{5}{-4}$$

Whakawehe -5 ki te -4.

$$t=\frac{5}{4}$$

Nā, me whakaoti te whārite t=\frac{-10±5}{-4} ina he tango te ±. Tango 5 mai i -10.

$$t=-\frac{15}{-4}$$

Whakawehe -15 ki te -4.

$$t=\frac{15}{4}$$

Kua oti te whārite te whakatau.

$$t=\frac{5}{4} t=\frac{15}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 10-2t ki te t.

$$10t-2t^{2}=9.375$$

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.

$$-2t^{2}+10t=9.375$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2t^{2}+10t}{-2}=\frac{9.375}{-2}$$

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

$$t^{2}+\frac{10}{-2}t=\frac{9.375}{-2}$$

Whakawehe 10 ki te -2.

$$t^{2}-5t=\frac{9.375}{-2}$$

Whakawehe 9.375 ki te -2.

$$t^{2}-5t=-4.6875$$

Whakawehea te -5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{2}. Nā, tāpiria te pūrua o te -\frac{5}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-5t+\left(-\frac{5}{2}\right)^{2}=-4.6875+\left(-\frac{5}{2}\right)^{2}$$

Pūruatia -\frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-5t+\frac{25}{4}=-4.6875+\frac{25}{4}$$

Tāpiri -4.6875 ki te \frac{25}{4} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$t^{2}-5t+\frac{25}{4}=\frac{25}{16}$$

Tauwehea te t^{2}-5t+\frac{25}{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}.

$$\left(t-\frac{5}{2}\right)^{2}=\frac{25}{16}$$

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

$$\sqrt{\left(t-\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{16}}$$

Whakarūnātia.

$$t-\frac{5}{2}=\frac{5}{4} t-\frac{5}{2}=-\frac{5}{4}$$

Me tāpiri \frac{5}{2} ki ngā taha e rua o te whārite.

$$t=\frac{15}{4} t=\frac{5}{4}$$