Whakaoti i te 6x^2+42x

$$6 x ^ { 2 } + 42 x$$

Tauwehe

$$6x\left(x+7\right)$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(x^{2}+7x\right)$$

Whakaarohia te x^{2}+7x. Tauwehea te x.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$6x\left(x+7\right)$$

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.

$$6x^{2}+42x=0$$

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.

$$x=\frac{-42±\sqrt{42^{2}}}{2\times 6}$$

Tuhia te pūtakerua o te 42^{2}.

$$x=\frac{-42±42}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-42±42}{12}$$

Nā, me whakaoti te whārite x=\frac{-42±42}{12} ina he tāpiri te ±. Tāpiri -42 ki te 42.

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

Whakawehe 0 ki te 12.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-42±42}{12} ina he tango te ±. Tango 42 mai i -42.

$$x=-\frac{84}{12}$$

Whakawehe -84 ki te 12.

$$x=-7$$

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 -7 mō te x_{2}.

$$6x^{2}+42x=6x\left(x-\left(-7\right)\right)$$

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

$$6x^{2}+42x=6x\left(x+7\right)$$

Aromātai

$$6x\left(x+7\right)$$