Whakaoti i te 5x^2+100x

$$5 x ^ { 2 } + 100 x$$

Tauwehe

$$5x\left(x+20\right)$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(x^{2}+20x\right)$$

Whakaarohia te x^{2}+20x. Tauwehea te x.

$$x\left(x+20\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5x\left(x+20\right)$$

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.

$$5x^{2}+100x=0$$

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.

$$x=\frac{-100±\sqrt{100^{2}}}{2\times 5}$$

Tuhia te pūtakerua o te 100^{2}.

$$x=\frac{-100±100}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-100±100}{10}$$

Nā, me whakaoti te whārite x=\frac{-100±100}{10} ina he tāpiri te ±. Tāpiri -100 ki te 100.

$$x=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-100±100}{10} ina he tango te ±. Tango 100 mai i -100.

$$x=-\frac{200}{10}$$

Whakawehe -200 ki te 10.

$$x=-20$$

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 0 mō te x_{1} me te -20 mō te x_{2}.

$$5x^{2}+100x=5x\left(x-\left(-20\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$5x^{2}+100x=5x\left(x+20\right)$$

Aromātai

$$5x\left(x+20\right)$$