Whakaoti i te 5w^2-40w-50

$$5 w ^ { 2 } - 40 w - 50$$

Tauwehe

$$5\left(w-\left(4-\sqrt{26}\right)\right)\left(w-\left(\sqrt{26}+4\right)\right)$$

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.

$$5w^{2}-40w-50=0$$

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.

$$w=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\times 5\left(-50\right)}}{2\times 5}$$

Pūrua -40.

$$w=\frac{-\left(-40\right)±\sqrt{1600-4\times 5\left(-50\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$w=\frac{-\left(-40\right)±\sqrt{1600-20\left(-50\right)}}{2\times 5}$$

Whakareatia -20 ki te -50.

$$w=\frac{-\left(-40\right)±\sqrt{1600+1000}}{2\times 5}$$

Tāpiri 1600 ki te 1000.

$$w=\frac{-\left(-40\right)±\sqrt{2600}}{2\times 5}$$

Tuhia te pūtakerua o te 2600.

$$w=\frac{-\left(-40\right)±10\sqrt{26}}{2\times 5}$$

Ko te tauaro o -40 ko 40.

$$w=\frac{40±10\sqrt{26}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$w=\frac{40±10\sqrt{26}}{10}$$

Nā, me whakaoti te whārite w=\frac{40±10\sqrt{26}}{10} ina he tāpiri te ±. Tāpiri 40 ki te 10\sqrt{26}.

$$w=\frac{10\sqrt{26}+40}{10}$$

Whakawehe 40+10\sqrt{26} ki te 10.

$$w=\sqrt{26}+4$$

Nā, me whakaoti te whārite w=\frac{40±10\sqrt{26}}{10} ina he tango te ±. Tango 10\sqrt{26} mai i 40.

$$w=\frac{40-10\sqrt{26}}{10}$$

Whakawehe 40-10\sqrt{26} ki te 10.

$$w=4-\sqrt{26}$$

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 4+\sqrt{26} mō te x_{1} me te 4-\sqrt{26} mō te x_{2}.

$$5w^{2}-40w-50=5\left(w-\left(\sqrt{26}+4\right)\right)\left(w-\left(4-\sqrt{26}\right)\right)$$

Aromātai

$$5\left(w^{2}-8w-10\right)$$