Whakaoti i te 15x^2-141x+90

$$15 { x }^{ 2 } -141x+90$$

Tauwehe

$$15\left(x-\frac{47-\sqrt{1609}}{10}\right)\left(x-\frac{\sqrt{1609}+47}{10}\right)$$

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.

$$15x^{2}-141x+90=0$$

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.

$$x=\frac{-\left(-141\right)±\sqrt{\left(-141\right)^{2}-4\times 15\times 90}}{2\times 15}$$

Pūrua -141.

$$x=\frac{-\left(-141\right)±\sqrt{19881-4\times 15\times 90}}{2\times 15}$$

Whakareatia -4 ki te 15.

$$x=\frac{-\left(-141\right)±\sqrt{19881-60\times 90}}{2\times 15}$$

Whakareatia -60 ki te 90.

$$x=\frac{-\left(-141\right)±\sqrt{19881-5400}}{2\times 15}$$

Tāpiri 19881 ki te -5400.

$$x=\frac{-\left(-141\right)±\sqrt{14481}}{2\times 15}$$

Tuhia te pūtakerua o te 14481.

$$x=\frac{-\left(-141\right)±3\sqrt{1609}}{2\times 15}$$

Ko te tauaro o -141 ko 141.

$$x=\frac{141±3\sqrt{1609}}{2\times 15}$$

Whakareatia 2 ki te 15.

$$x=\frac{141±3\sqrt{1609}}{30}$$

Nā, me whakaoti te whārite x=\frac{141±3\sqrt{1609}}{30} ina he tāpiri te ±. Tāpiri 141 ki te 3\sqrt{1609}.

$$x=\frac{3\sqrt{1609}+141}{30}$$

Whakawehe 141+3\sqrt{1609} ki te 30.

$$x=\frac{\sqrt{1609}+47}{10}$$

Nā, me whakaoti te whārite x=\frac{141±3\sqrt{1609}}{30} ina he tango te ±. Tango 3\sqrt{1609} mai i 141.

$$x=\frac{141-3\sqrt{1609}}{30}$$

Whakawehe 141-3\sqrt{1609} ki te 30.

$$x=\frac{47-\sqrt{1609}}{10}$$

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{47+\sqrt{1609}}{10} mō te x_{1} me te \frac{47-\sqrt{1609}}{10} mō te x_{2}.

$$15x^{2}-141x+90=15\left(x-\frac{\sqrt{1609}+47}{10}\right)\left(x-\frac{47-\sqrt{1609}}{10}\right)$$

Aromātai

$$15x^{2}-141x+90$$