Whakaoti i te -16x^2+5184x+421

$$- 16 x ^ { 2 } + 5184 x + 421$$

Tauwehe

$$-16\left(x-\left(-\frac{5\sqrt{16813}}{4}+162\right)\right)\left(x-\left(\frac{5\sqrt{16813}}{4}+162\right)\right)$$

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.

$$-16x^{2}+5184x+421=0$$

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.

$$x=\frac{-5184±\sqrt{5184^{2}-4\left(-16\right)\times 421}}{2\left(-16\right)}$$

Pūrua 5184.

$$x=\frac{-5184±\sqrt{26873856-4\left(-16\right)\times 421}}{2\left(-16\right)}$$

Whakareatia -4 ki te -16.

$$x=\frac{-5184±\sqrt{26873856+64\times 421}}{2\left(-16\right)}$$

Whakareatia 64 ki te 421.

$$x=\frac{-5184±\sqrt{26873856+26944}}{2\left(-16\right)}$$

Tāpiri 26873856 ki te 26944.

$$x=\frac{-5184±\sqrt{26900800}}{2\left(-16\right)}$$

Tuhia te pūtakerua o te 26900800.

$$x=\frac{-5184±40\sqrt{16813}}{2\left(-16\right)}$$

Whakareatia 2 ki te -16.

$$x=\frac{-5184±40\sqrt{16813}}{-32}$$

Nā, me whakaoti te whārite x=\frac{-5184±40\sqrt{16813}}{-32} ina he tāpiri te ±. Tāpiri -5184 ki te 40\sqrt{16813}.

$$x=\frac{40\sqrt{16813}-5184}{-32}$$

Whakawehe -5184+40\sqrt{16813} ki te -32.

$$x=-\frac{5\sqrt{16813}}{4}+162$$

Nā, me whakaoti te whārite x=\frac{-5184±40\sqrt{16813}}{-32} ina he tango te ±. Tango 40\sqrt{16813} mai i -5184.

$$x=\frac{-40\sqrt{16813}-5184}{-32}$$

Whakawehe -5184-40\sqrt{16813} ki te -32.

$$x=\frac{5\sqrt{16813}}{4}+162$$

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 162-\frac{5\sqrt{16813}}{4} mō te x_{1} me te 162+\frac{5\sqrt{16813}}{4} mō te x_{2}.

$$-16x^{2}+5184x+421=-16\left(x-\left(-\frac{5\sqrt{16813}}{4}+162\right)\right)\left(x-\left(\frac{5\sqrt{16813}}{4}+162\right)\right)$$

Aromātai

$$421+5184x-16x^{2}$$