Whakaoti i te -49t^2+2t-10=0

$$- 49 t ^ { 2 } + 2 t - 10 = 0$$

Whakaoti mō t

$$t=\frac{-\sqrt{489}i+1}{49}\approx 0.020408163-0.451292743i$$

$$t=\frac{1+\sqrt{489}i}{49}\approx 0.020408163+0.451292743i$$

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.

$$-49t^{2}+2t-10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -49 mō a, 2 mō b, me -10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-2±\sqrt{2^{2}-4\left(-49\right)\left(-10\right)}}{2\left(-49\right)}$$

Pūrua 2.

$$t=\frac{-2±\sqrt{4-4\left(-49\right)\left(-10\right)}}{2\left(-49\right)}$$

Whakareatia -4 ki te -49.

$$t=\frac{-2±\sqrt{4+196\left(-10\right)}}{2\left(-49\right)}$$

Whakareatia 196 ki te -10.

$$t=\frac{-2±\sqrt{4-1960}}{2\left(-49\right)}$$

Tāpiri 4 ki te -1960.

$$t=\frac{-2±\sqrt{-1956}}{2\left(-49\right)}$$

Tuhia te pūtakerua o te -1956.

$$t=\frac{-2±2\sqrt{489}i}{2\left(-49\right)}$$

Whakareatia 2 ki te -49.

$$t=\frac{-2±2\sqrt{489}i}{-98}$$

Nā, me whakaoti te whārite t=\frac{-2±2\sqrt{489}i}{-98} ina he tāpiri te ±. Tāpiri -2 ki te 2i\sqrt{489}.

$$t=\frac{-2+2\sqrt{489}i}{-98}$$

Whakawehe -2+2i\sqrt{489} ki te -98.

$$t=\frac{-\sqrt{489}i+1}{49}$$

Nā, me whakaoti te whārite t=\frac{-2±2\sqrt{489}i}{-98} ina he tango te ±. Tango 2i\sqrt{489} mai i -2.

$$t=\frac{-2\sqrt{489}i-2}{-98}$$

Whakawehe -2-2i\sqrt{489} ki te -98.

$$t=\frac{1+\sqrt{489}i}{49}$$

Kua oti te whārite te whakatau.

$$t=\frac{-\sqrt{489}i+1}{49} t=\frac{1+\sqrt{489}i}{49}$$

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.

$$-49t^{2}+2t-10=0$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$-49t^{2}+2t-10-\left(-10\right)=-\left(-10\right)$$

Mā te tango i te -10 i a ia ake anō ka toe ko te 0.

$$-49t^{2}+2t=-\left(-10\right)$$

Tango -10 mai i 0.

$$-49t^{2}+2t=10$$

Whakawehea ngā taha e rua ki te -49.

$$\frac{-49t^{2}+2t}{-49}=\frac{10}{-49}$$

Mā te whakawehe ki te -49 ka wetekia te whakareanga ki te -49.

$$t^{2}+\frac{2}{-49}t=\frac{10}{-49}$$

Whakawehe 2 ki te -49.

$$t^{2}-\frac{2}{49}t=\frac{10}{-49}$$

Whakawehe 10 ki te -49.

$$t^{2}-\frac{2}{49}t=-\frac{10}{49}$$

Whakawehea te -\frac{2}{49}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{49}. Nā, tāpiria te pūrua o te -\frac{1}{49} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{2}{49}t+\left(-\frac{1}{49}\right)^{2}=-\frac{10}{49}+\left(-\frac{1}{49}\right)^{2}$$

Pūruatia -\frac{1}{49} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{2}{49}t+\frac{1}{2401}=-\frac{10}{49}+\frac{1}{2401}$$

Tāpiri -\frac{10}{49} ki te \frac{1}{2401} 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.

$$t^{2}-\frac{2}{49}t+\frac{1}{2401}=-\frac{489}{2401}$$

Tauwehea t^{2}-\frac{2}{49}t+\frac{1}{2401}. 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}.

$$\left(t-\frac{1}{49}\right)^{2}=-\frac{489}{2401}$$

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

$$\sqrt{\left(t-\frac{1}{49}\right)^{2}}=\sqrt{-\frac{489}{2401}}$$

Whakarūnātia.

$$t-\frac{1}{49}=\frac{\sqrt{489}i}{49} t-\frac{1}{49}=-\frac{\sqrt{489}i}{49}$$

Me tāpiri \frac{1}{49} ki ngā taha e rua o te whārite.

$$t=\frac{1+\sqrt{489}i}{49} t=\frac{-\sqrt{489}i+1}{49}$$