Whakaoti i te 300q-2q^2-100-q^2

$$300 q - 2 q ^ { 2 } - 100 - q ^ { 2 }$$

Tauwehe

$$-3\left(q-\left(-\frac{10\sqrt{222}}{3}+50\right)\right)\left(q-\left(\frac{10\sqrt{222}}{3}+50\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -2q^{2} me -q^{2}, ka -3q^{2}.

$$factor(300q-3q^{2}-100)$$

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.

$$-3q^{2}+300q-100=0$$

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.

$$q=\frac{-300±\sqrt{300^{2}-4\left(-3\right)\left(-100\right)}}{2\left(-3\right)}$$

Pūrua 300.

$$q=\frac{-300±\sqrt{90000-4\left(-3\right)\left(-100\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$q=\frac{-300±\sqrt{90000+12\left(-100\right)}}{2\left(-3\right)}$$

Whakareatia 12 ki te -100.

$$q=\frac{-300±\sqrt{90000-1200}}{2\left(-3\right)}$$

Tāpiri 90000 ki te -1200.

$$q=\frac{-300±\sqrt{88800}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 88800.

$$q=\frac{-300±20\sqrt{222}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$q=\frac{-300±20\sqrt{222}}{-6}$$

Nā, me whakaoti te whārite q=\frac{-300±20\sqrt{222}}{-6} ina he tāpiri te ±. Tāpiri -300 ki te 20\sqrt{222}.

$$q=\frac{20\sqrt{222}-300}{-6}$$

Whakawehe -300+20\sqrt{222} ki te -6.

$$q=-\frac{10\sqrt{222}}{3}+50$$

Nā, me whakaoti te whārite q=\frac{-300±20\sqrt{222}}{-6} ina he tango te ±. Tango 20\sqrt{222} mai i -300.

$$q=\frac{-20\sqrt{222}-300}{-6}$$

Whakawehe -300-20\sqrt{222} ki te -6.

$$q=\frac{10\sqrt{222}}{3}+50$$

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 50-\frac{10\sqrt{222}}{3} mō te x_{1} me te 50+\frac{10\sqrt{222}}{3} mō te x_{2}.

$$-3q^{2}+300q-100=-3\left(q-\left(-\frac{10\sqrt{222}}{3}+50\right)\right)\left(q-\left(\frac{10\sqrt{222}}{3}+50\right)\right)$$

Aromātai

$$-3q^{2}+300q-100$$

Ngā Upane Otinga

Pahekotia te -2q^{2} me -q^{2}, ka -3q^{2}.

$$300q-3q^{2}-100$$