Whakaoti i te 18x^2+600-230x

$$18 { x }^{ 2 } +600-230x$$

Tauwehe

$$18\left(x-\frac{115-5\sqrt{97}}{18}\right)\left(x-\frac{5\sqrt{97}+115}{18}\right)$$

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.

$$18x^{2}-230x+600=0$$

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.

$$x=\frac{-\left(-230\right)±\sqrt{\left(-230\right)^{2}-4\times 18\times 600}}{2\times 18}$$

Pūrua -230.

$$x=\frac{-\left(-230\right)±\sqrt{52900-4\times 18\times 600}}{2\times 18}$$

Whakareatia -4 ki te 18.

$$x=\frac{-\left(-230\right)±\sqrt{52900-72\times 600}}{2\times 18}$$

Whakareatia -72 ki te 600.

$$x=\frac{-\left(-230\right)±\sqrt{52900-43200}}{2\times 18}$$

Tāpiri 52900 ki te -43200.

$$x=\frac{-\left(-230\right)±\sqrt{9700}}{2\times 18}$$

Tuhia te pūtakerua o te 9700.

$$x=\frac{-\left(-230\right)±10\sqrt{97}}{2\times 18}$$

Ko te tauaro o -230 ko 230.

$$x=\frac{230±10\sqrt{97}}{2\times 18}$$

Whakareatia 2 ki te 18.

$$x=\frac{230±10\sqrt{97}}{36}$$

Nā, me whakaoti te whārite x=\frac{230±10\sqrt{97}}{36} ina he tāpiri te ±. Tāpiri 230 ki te 10\sqrt{97}.

$$x=\frac{10\sqrt{97}+230}{36}$$

Whakawehe 230+10\sqrt{97} ki te 36.

$$x=\frac{5\sqrt{97}+115}{18}$$

Nā, me whakaoti te whārite x=\frac{230±10\sqrt{97}}{36} ina he tango te ±. Tango 10\sqrt{97} mai i 230.

$$x=\frac{230-10\sqrt{97}}{36}$$

Whakawehe 230-10\sqrt{97} ki te 36.

$$x=\frac{115-5\sqrt{97}}{18}$$

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{115+5\sqrt{97}}{18} mō te x_{1} me te \frac{115-5\sqrt{97}}{18} mō te x_{2}.

$$18x^{2}-230x+600=18\left(x-\frac{5\sqrt{97}+115}{18}\right)\left(x-\frac{115-5\sqrt{97}}{18}\right)$$

Aromātai

$$18x^{2}-230x+600$$