Whakaoti i te 5v^2+30v-70

$$5 v ^ { 2 } + 30 v - 70$$

Tauwehe

$$5\left(v-\left(-\sqrt{23}-3\right)\right)\left(v-\left(\sqrt{23}-3\right)\right)$$

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.

$$5v^{2}+30v-70=0$$

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.

$$v=\frac{-30±\sqrt{30^{2}-4\times 5\left(-70\right)}}{2\times 5}$$

Pūrua 30.

$$v=\frac{-30±\sqrt{900-4\times 5\left(-70\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$v=\frac{-30±\sqrt{900-20\left(-70\right)}}{2\times 5}$$

Whakareatia -20 ki te -70.

$$v=\frac{-30±\sqrt{900+1400}}{2\times 5}$$

Tāpiri 900 ki te 1400.

$$v=\frac{-30±\sqrt{2300}}{2\times 5}$$

Tuhia te pūtakerua o te 2300.

$$v=\frac{-30±10\sqrt{23}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$v=\frac{-30±10\sqrt{23}}{10}$$

Nā, me whakaoti te whārite v=\frac{-30±10\sqrt{23}}{10} ina he tāpiri te ±. Tāpiri -30 ki te 10\sqrt{23}.

$$v=\frac{10\sqrt{23}-30}{10}$$

Whakawehe -30+10\sqrt{23} ki te 10.

$$v=\sqrt{23}-3$$

Nā, me whakaoti te whārite v=\frac{-30±10\sqrt{23}}{10} ina he tango te ±. Tango 10\sqrt{23} mai i -30.

$$v=\frac{-10\sqrt{23}-30}{10}$$

Whakawehe -30-10\sqrt{23} ki te 10.

$$v=-\sqrt{23}-3$$

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 -3+\sqrt{23} mō te x_{1} me te -3-\sqrt{23} mō te x_{2}.

$$5v^{2}+30v-70=5\left(v-\left(\sqrt{23}-3\right)\right)\left(v-\left(-\sqrt{23}-3\right)\right)$$

Aromātai

$$5\left(v^{2}+6v-14\right)$$