Whakaoti i te [10-5t)t=9.375

$$[ 10 - 5 t ) t = 9.375$$

Whakaoti mō t

$$t=\frac{i\sqrt{14}}{4}+1\approx 1+0.935414347i$$

$$t=-\frac{i\sqrt{14}}{4}+1\approx 1-0.935414347i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 10-5t ki te t.

$$10t-5t^{2}=9.375$$

Tangohia te 9.375 mai i ngā taha e rua.

$$10t-5t^{2}-9.375=0$$

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.

$$-5t^{2}+10t-9.375=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 10 mō b, me -9.375 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-10±\sqrt{10^{2}-4\left(-5\right)\left(-9.375\right)}}{2\left(-5\right)}$$

Pūrua 10.

$$t=\frac{-10±\sqrt{100-4\left(-5\right)\left(-9.375\right)}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$t=\frac{-10±\sqrt{100+20\left(-9.375\right)}}{2\left(-5\right)}$$

Whakareatia 20 ki te -9.375.

$$t=\frac{-10±\sqrt{100-187.5}}{2\left(-5\right)}$$

Tāpiri 100 ki te -187.5.

$$t=\frac{-10±\sqrt{-87.5}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te -87.5.

$$t=\frac{-10±\frac{5\sqrt{14}i}{2}}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$t=\frac{-10±\frac{5\sqrt{14}i}{2}}{-10}$$

Nā, me whakaoti te whārite t=\frac{-10±\frac{5\sqrt{14}i}{2}}{-10} ina he tāpiri te ±. Tāpiri -10 ki te \frac{5i\sqrt{14}}{2}.

$$t=\frac{\frac{5\sqrt{14}i}{2}-10}{-10}$$

Whakawehe -10+\frac{5i\sqrt{14}}{2} ki te -10.

$$t=-\frac{\sqrt{14}i}{4}+1$$

Nā, me whakaoti te whārite t=\frac{-10±\frac{5\sqrt{14}i}{2}}{-10} ina he tango te ±. Tango \frac{5i\sqrt{14}}{2} mai i -10.

$$t=\frac{-\frac{5\sqrt{14}i}{2}-10}{-10}$$

Whakawehe -10-\frac{5i\sqrt{14}}{2} ki te -10.

$$t=\frac{\sqrt{14}i}{4}+1$$

Kua oti te whārite te whakatau.

$$t=-\frac{\sqrt{14}i}{4}+1 t=\frac{\sqrt{14}i}{4}+1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 10-5t ki te t.

$$10t-5t^{2}=9.375$$

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.

$$-5t^{2}+10t=9.375$$

Whakawehea ngā taha e rua ki te -5.

$$\frac{-5t^{2}+10t}{-5}=\frac{9.375}{-5}$$

Mā te whakawehe ki te -5 ka wetekia te whakareanga ki te -5.

$$t^{2}+\frac{10}{-5}t=\frac{9.375}{-5}$$

Whakawehe 10 ki te -5.

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

Whakawehe 9.375 ki te -5.

$$t^{2}-2t=-1.875$$

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.

$$t^{2}-2t+1=-1.875+1$$

Tāpiri -1.875 ki te 1.

$$t^{2}-2t+1=-0.875$$

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

$$\left(t-1\right)^{2}=-0.875$$

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

$$\sqrt{\left(t-1\right)^{2}}=\sqrt{-0.875}$$

Whakarūnātia.

$$t-1=\frac{\sqrt{14}i}{4} t-1=-\frac{\sqrt{14}i}{4}$$

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

$$t=\frac{\sqrt{14}i}{4}+1 t=-\frac{\sqrt{14}i}{4}+1$$