Whakaoti i te 7x+14x^2

$$7x+14 { x }^{ 2 }$$

Tauwehe

$$7x\left(2x+1\right)$$

Ngā Upane Otinga

Tauwehea te 7.

$$7\left(x+2x^{2}\right)$$

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

$$x\left(1+2x\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$7x\left(2x+1\right)$$

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.

$$14x^{2}+7x=0$$

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.

$$x=\frac{-7±\sqrt{7^{2}}}{2\times 14}$$

Tuhia te pūtakerua o te 7^{2}.

$$x=\frac{-7±7}{2\times 14}$$

Whakareatia 2 ki te 14.

$$x=\frac{-7±7}{28}$$

Nā, me whakaoti te whārite x=\frac{-7±7}{28} ina he tāpiri te ±. Tāpiri -7 ki te 7.

$$x=\frac{0}{28}$$

Whakawehe 0 ki te 28.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-7±7}{28} ina he tango te ±. Tango 7 mai i -7.

$$x=-\frac{14}{28}$$

Whakahekea te hautanga \frac{-14}{28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$x=-\frac{1}{2}$$

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 -\frac{1}{2} mō te x_{2}.

$$14x^{2}+7x=14x\left(x-\left(-\frac{1}{2}\right)\right)$$

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

$$14x^{2}+7x=14x\left(x+\frac{1}{2}\right)$$

Tāpiri \frac{1}{2} ki te x mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$14x^{2}+7x=14x\times \frac{2x+1}{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 14 me te 2.

$$14x^{2}+7x=7x\left(2x+1\right)$$

Aromātai

$$7x\left(2x+1\right)$$