Whakaoti i te 30x^2+10x

$$30 x ^ { 2 } + 10 x$$

Tauwehe

$$10x\left(3x+1\right)$$

Ngā Upane Otinga

Tauwehea te 10.

$$10\left(3x^{2}+x\right)$$

Whakaarohia te 3x^{2}+x. Tauwehea te x.

$$x\left(3x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$10x\left(3x+1\right)$$

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.

$$30x^{2}+10x=0$$

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.

$$x=\frac{-10±\sqrt{10^{2}}}{2\times 30}$$

Tuhia te pūtakerua o te 10^{2}.

$$x=\frac{-10±10}{2\times 30}$$

Whakareatia 2 ki te 30.

$$x=\frac{-10±10}{60}$$

Nā, me whakaoti te whārite x=\frac{-10±10}{60} ina he tāpiri te ±. Tāpiri -10 ki te 10.

$$x=\frac{0}{60}$$

Whakawehe 0 ki te 60.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-10±10}{60} ina he tango te ±. Tango 10 mai i -10.

$$x=-\frac{20}{60}$$

Whakahekea te hautanga \frac{-20}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$x=-\frac{1}{3}$$

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 0 mō te x_{1} me te -\frac{1}{3} mō te x_{2}.

$$30x^{2}+10x=30x\left(x-\left(-\frac{1}{3}\right)\right)$$

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

$$30x^{2}+10x=30x\left(x+\frac{1}{3}\right)$$

Tāpiri \frac{1}{3} 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.

$$30x^{2}+10x=30x\times \frac{3x+1}{3}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 30 me te 3.

$$30x^{2}+10x=10x\left(3x+1\right)$$

Aromātai

$$10x\left(3x+1\right)$$