Whakaoti i te 25a^2-520a-2860

$$25 a ^ { 2 } - 520 a - 2860$$

Tauwehe

$$25\left(a-\frac{52-2\sqrt{1391}}{5}\right)\left(a-\frac{2\sqrt{1391}+52}{5}\right)$$

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.

$$25a^{2}-520a-2860=0$$

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.

$$a=\frac{-\left(-520\right)±\sqrt{\left(-520\right)^{2}-4\times 25\left(-2860\right)}}{2\times 25}$$

Pūrua -520.

$$a=\frac{-\left(-520\right)±\sqrt{270400-4\times 25\left(-2860\right)}}{2\times 25}$$

Whakareatia -4 ki te 25.

$$a=\frac{-\left(-520\right)±\sqrt{270400-100\left(-2860\right)}}{2\times 25}$$

Whakareatia -100 ki te -2860.

$$a=\frac{-\left(-520\right)±\sqrt{270400+286000}}{2\times 25}$$

Tāpiri 270400 ki te 286000.

$$a=\frac{-\left(-520\right)±\sqrt{556400}}{2\times 25}$$

Tuhia te pūtakerua o te 556400.

$$a=\frac{-\left(-520\right)±20\sqrt{1391}}{2\times 25}$$

Ko te tauaro o -520 ko 520.

$$a=\frac{520±20\sqrt{1391}}{2\times 25}$$

Whakareatia 2 ki te 25.

$$a=\frac{520±20\sqrt{1391}}{50}$$

Nā, me whakaoti te whārite a=\frac{520±20\sqrt{1391}}{50} ina he tāpiri te ±. Tāpiri 520 ki te 20\sqrt{1391}.

$$a=\frac{20\sqrt{1391}+520}{50}$$

Whakawehe 520+20\sqrt{1391} ki te 50.

$$a=\frac{2\sqrt{1391}+52}{5}$$

Nā, me whakaoti te whārite a=\frac{520±20\sqrt{1391}}{50} ina he tango te ±. Tango 20\sqrt{1391} mai i 520.

$$a=\frac{520-20\sqrt{1391}}{50}$$

Whakawehe 520-20\sqrt{1391} ki te 50.

$$a=\frac{52-2\sqrt{1391}}{5}$$

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{52+2\sqrt{1391}}{5} mō te x_{1} me te \frac{52-2\sqrt{1391}}{5} mō te x_{2}.

$$25a^{2}-520a-2860=25\left(a-\frac{2\sqrt{1391}+52}{5}\right)\left(a-\frac{52-2\sqrt{1391}}{5}\right)$$

Aromātai

$$25a^{2}-520a-2860$$