Whakaoti i te 5x^2+3x-100

$$5 x ^ { 2 } + 3 x - 100$$

Tauwehe

$$5\left(x-\frac{-7\sqrt{41}-3}{10}\right)\left(x-\frac{7\sqrt{41}-3}{10}\right)$$

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.

$$5x^{2}+3x-100=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 5\left(-100\right)}}{2\times 5}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\times 5\left(-100\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-3±\sqrt{9-20\left(-100\right)}}{2\times 5}$$

Whakareatia -20 ki te -100.

$$x=\frac{-3±\sqrt{9+2000}}{2\times 5}$$

Tāpiri 9 ki te 2000.

$$x=\frac{-3±\sqrt{2009}}{2\times 5}$$

Tuhia te pūtakerua o te 2009.

$$x=\frac{-3±7\sqrt{41}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-3±7\sqrt{41}}{10}$$

Nā, me whakaoti te whārite x=\frac{-3±7\sqrt{41}}{10} ina he tāpiri te ±. Tāpiri -3 ki te 7\sqrt{41}.

$$x=\frac{7\sqrt{41}-3}{10}$$

Nā, me whakaoti te whārite x=\frac{-3±7\sqrt{41}}{10} ina he tango te ±. Tango 7\sqrt{41} mai i -3.

$$x=\frac{-7\sqrt{41}-3}{10}$$

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{-3+7\sqrt{41}}{10} mō te x_{1} me te \frac{-3-7\sqrt{41}}{10} mō te x_{2}.

$$5x^{2}+3x-100=5\left(x-\frac{7\sqrt{41}-3}{10}\right)\left(x-\frac{-7\sqrt{41}-3}{10}\right)$$

Aromātai

$$5x^{2}+3x-100$$