Whakaoti i te 31a^2-837a-7290

$$31 a ^ { 2 } - 837 a - 7290$$

Tauwehe

$$31\left(a-\left(-\frac{27\sqrt{2201}}{62}+\frac{27}{2}\right)\right)\left(a-\left(\frac{27\sqrt{2201}}{62}+\frac{27}{2}\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$31a^{2}-837a-7290=0$$

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.

$$a=\frac{-\left(-837\right)±\sqrt{\left(-837\right)^{2}-4\times 31\left(-7290\right)}}{2\times 31}$$

Pūrua -837.

$$a=\frac{-\left(-837\right)±\sqrt{700569-4\times 31\left(-7290\right)}}{2\times 31}$$

Whakareatia -4 ki te 31.

$$a=\frac{-\left(-837\right)±\sqrt{700569-124\left(-7290\right)}}{2\times 31}$$

Whakareatia -124 ki te -7290.

$$a=\frac{-\left(-837\right)±\sqrt{700569+903960}}{2\times 31}$$

Tāpiri 700569 ki te 903960.

$$a=\frac{-\left(-837\right)±\sqrt{1604529}}{2\times 31}$$

Tuhia te pūtakerua o te 1604529.

$$a=\frac{-\left(-837\right)±27\sqrt{2201}}{2\times 31}$$

Ko te tauaro o -837 ko 837.

$$a=\frac{837±27\sqrt{2201}}{2\times 31}$$

Whakareatia 2 ki te 31.

$$a=\frac{837±27\sqrt{2201}}{62}$$

Nā, me whakaoti te whārite a=\frac{837±27\sqrt{2201}}{62} ina he tāpiri te ±. Tāpiri 837 ki te 27\sqrt{2201}.

$$a=\frac{27\sqrt{2201}+837}{62}$$

Whakawehe 837+27\sqrt{2201} ki te 62.

$$a=\frac{27\sqrt{2201}}{62}+\frac{27}{2}$$

Nā, me whakaoti te whārite a=\frac{837±27\sqrt{2201}}{62} ina he tango te ±. Tango 27\sqrt{2201} mai i 837.

$$a=\frac{837-27\sqrt{2201}}{62}$$

Whakawehe 837-27\sqrt{2201} ki te 62.

$$a=-\frac{27\sqrt{2201}}{62}+\frac{27}{2}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{27}{2}+\frac{27\sqrt{2201}}{62} mō te x_{1} me te \frac{27}{2}-\frac{27\sqrt{2201}}{62} mō te x_{2}.

$$31a^{2}-837a-7290=31\left(a-\left(\frac{27\sqrt{2201}}{62}+\frac{27}{2}\right)\right)\left(a-\left(-\frac{27\sqrt{2201}}{62}+\frac{27}{2}\right)\right)$$

Aromātai

$$31a^{2}-837a-7290$$