Whakaoti i te 6x^2+15x

$$6 x ^ { 2 } + 15 x$$

Tauwehe

$$3x\left(2x+5\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(2x^{2}+5x\right)$$

Whakaarohia te 2x^{2}+5x. Tauwehea te x.

$$x\left(2x+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3x\left(2x+5\right)$$

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.

$$6x^{2}+15x=0$$

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.

$$x=\frac{-15±\sqrt{15^{2}}}{2\times 6}$$

Tuhia te pūtakerua o te 15^{2}.

$$x=\frac{-15±15}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-15±15}{12}$$

Nā, me whakaoti te whārite x=\frac{-15±15}{12} ina he tāpiri te ±. Tāpiri -15 ki te 15.

$$x=\frac{0}{12}$$

Whakawehe 0 ki te 12.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-15±15}{12} ina he tango te ±. Tango 15 mai i -15.

$$x=-\frac{30}{12}$$

Whakahekea te hautanga \frac{-30}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=-\frac{5}{2}$$

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{5}{2} mō te x_{2}.

$$6x^{2}+15x=6x\left(x-\left(-\frac{5}{2}\right)\right)$$

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

$$6x^{2}+15x=6x\left(x+\frac{5}{2}\right)$$

Tāpiri \frac{5}{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.

$$6x^{2}+15x=6x\times \frac{2x+5}{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 6 me te 2.

$$6x^{2}+15x=3x\left(2x+5\right)$$

Aromātai

$$3x\left(2x+5\right)$$