Whakaoti i te 2z^2+2z-60

$$2 z ^ { 2 } + 2 z - 60$$

Tauwehe

$$2\left(z-5\right)\left(z+6\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(z^{2}+z-30\right)$$

Whakaarohia te z^{2}+z-30. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei z^{2}+az+bz-30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=1\left(-30\right)=-30$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -30.

$$-1,30 -2,15 -3,10 -5,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+30=29 -2+15=13 -3+10=7 -5+6=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-5 b=6$$

Tuhia anō te z^{2}+z-30 hei \left(z^{2}-5z\right)+\left(6z-30\right).

$$\left(z^{2}-5z\right)+\left(6z-30\right)$$

Tauwehea te z i te tuatahi me te 6 i te rōpū tuarua.

$$z\left(z-5\right)+6\left(z-5\right)$$

Whakatauwehea atu te kīanga pātahi z-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(z-5\right)\left(z+6\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(z-5\right)\left(z+6\right)$$

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.

$$2z^{2}+2z-60=0$$

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.

$$z=\frac{-2±\sqrt{2^{2}-4\times 2\left(-60\right)}}{2\times 2}$$

Pūrua 2.

$$z=\frac{-2±\sqrt{4-4\times 2\left(-60\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$z=\frac{-2±\sqrt{4-8\left(-60\right)}}{2\times 2}$$

Whakareatia -8 ki te -60.

$$z=\frac{-2±\sqrt{4+480}}{2\times 2}$$

Tāpiri 4 ki te 480.

$$z=\frac{-2±\sqrt{484}}{2\times 2}$$

Tuhia te pūtakerua o te 484.

$$z=\frac{-2±22}{2\times 2}$$

Whakareatia 2 ki te 2.

$$z=\frac{-2±22}{4}$$

Nā, me whakaoti te whārite z=\frac{-2±22}{4} ina he tāpiri te ±. Tāpiri -2 ki te 22.

$$z=\frac{20}{4}$$

Whakawehe 20 ki te 4.

$$z=5$$

Nā, me whakaoti te whārite z=\frac{-2±22}{4} ina he tango te ±. Tango 22 mai i -2.

$$z=-\frac{24}{4}$$

Whakawehe -24 ki te 4.

$$z=-6$$

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 5 mō te x_{1} me te -6 mō te x_{2}.

$$2z^{2}+2z-60=2\left(z-5\right)\left(z-\left(-6\right)\right)$$

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

$$2z^{2}+2z-60=2\left(z-5\right)\left(z+6\right)$$

Aromātai

$$2\left(z-5\right)\left(z+6\right)$$