Whakaoti i te 11*5x^2+82x-4

$$11 \cdot 5 x ^ { 2 } + 82 x - 4$$

Tauwehe

$$55\left(x-\frac{-\sqrt{1901}-41}{55}\right)\left(x-\frac{\sqrt{1901}-41}{55}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 11 ki te 5, ka 55.

$$factor(55x^{2}+82x-4)$$

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.

$$55x^{2}+82x-4=0$$

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.

$$x=\frac{-82±\sqrt{82^{2}-4\times 55\left(-4\right)}}{2\times 55}$$

Pūrua 82.

$$x=\frac{-82±\sqrt{6724-4\times 55\left(-4\right)}}{2\times 55}$$

Whakareatia -4 ki te 55.

$$x=\frac{-82±\sqrt{6724-220\left(-4\right)}}{2\times 55}$$

Whakareatia -220 ki te -4.

$$x=\frac{-82±\sqrt{6724+880}}{2\times 55}$$

Tāpiri 6724 ki te 880.

$$x=\frac{-82±\sqrt{7604}}{2\times 55}$$

Tuhia te pūtakerua o te 7604.

$$x=\frac{-82±2\sqrt{1901}}{2\times 55}$$

Whakareatia 2 ki te 55.

$$x=\frac{-82±2\sqrt{1901}}{110}$$

Nā, me whakaoti te whārite x=\frac{-82±2\sqrt{1901}}{110} ina he tāpiri te ±. Tāpiri -82 ki te 2\sqrt{1901}.

$$x=\frac{2\sqrt{1901}-82}{110}$$

Whakawehe -82+2\sqrt{1901} ki te 110.

$$x=\frac{\sqrt{1901}-41}{55}$$

Nā, me whakaoti te whārite x=\frac{-82±2\sqrt{1901}}{110} ina he tango te ±. Tango 2\sqrt{1901} mai i -82.

$$x=\frac{-2\sqrt{1901}-82}{110}$$

Whakawehe -82-2\sqrt{1901} ki te 110.

$$x=\frac{-\sqrt{1901}-41}{55}$$

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{-41+\sqrt{1901}}{55} mō te x_{1} me te \frac{-41-\sqrt{1901}}{55} mō te x_{2}.

$$55x^{2}+82x-4=55\left(x-\frac{\sqrt{1901}-41}{55}\right)\left(x-\frac{-\sqrt{1901}-41}{55}\right)$$

Aromātai

$$55x^{2}+82x-4$$

Ngā Upane Otinga

Whakareatia te 11 ki te 5, ka 55.

$$55x^{2}+82x-4$$