Whakaoti i te 202x^2-108109x+2491

$$202 x ^ { 2 } - 108109 x + 2491$$

Tauwehe

$$202\left(x-\frac{108109-\sqrt{11685543153}}{404}\right)\left(x-\frac{\sqrt{11685543153}+108109}{404}\right)$$

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.

$$202x^{2}-108109x+2491=0$$

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.

$$x=\frac{-\left(-108109\right)±\sqrt{\left(-108109\right)^{2}-4\times 202\times 2491}}{2\times 202}$$

Pūrua -108109.

$$x=\frac{-\left(-108109\right)±\sqrt{11687555881-4\times 202\times 2491}}{2\times 202}$$

Whakareatia -4 ki te 202.

$$x=\frac{-\left(-108109\right)±\sqrt{11687555881-808\times 2491}}{2\times 202}$$

Whakareatia -808 ki te 2491.

$$x=\frac{-\left(-108109\right)±\sqrt{11687555881-2012728}}{2\times 202}$$

Tāpiri 11687555881 ki te -2012728.

$$x=\frac{-\left(-108109\right)±\sqrt{11685543153}}{2\times 202}$$

Ko te tauaro o -108109 ko 108109.

$$x=\frac{108109±\sqrt{11685543153}}{2\times 202}$$

Whakareatia 2 ki te 202.

$$x=\frac{108109±\sqrt{11685543153}}{404}$$

Nā, me whakaoti te whārite x=\frac{108109±\sqrt{11685543153}}{404} ina he tāpiri te ±. Tāpiri 108109 ki te \sqrt{11685543153}.

$$x=\frac{\sqrt{11685543153}+108109}{404}$$

Nā, me whakaoti te whārite x=\frac{108109±\sqrt{11685543153}}{404} ina he tango te ±. Tango \sqrt{11685543153} mai i 108109.

$$x=\frac{108109-\sqrt{11685543153}}{404}$$

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{108109+\sqrt{11685543153}}{404} mō te x_{1} me te \frac{108109-\sqrt{11685543153}}{404} mō te x_{2}.

$$202x^{2}-108109x+2491=202\left(x-\frac{\sqrt{11685543153}+108109}{404}\right)\left(x-\frac{108109-\sqrt{11685543153}}{404}\right)$$

Aromātai

$$202x^{2}-108109x+2491$$