Whakaoti i te x^2+32x-273

$${ x }^{ 2 } +32x-273$$

Tauwehe

$$\left(x-7\right)\left(x+39\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-273. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=32 ab=1\left(-273\right)=-273$$

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 -273.

$$-1,273 -3,91 -7,39 -13,21$$

Tātaihia te tapeke mō ia takirua.

$$-1+273=272 -3+91=88 -7+39=32 -13+21=8$$

Ko te otinga te takirua ka hoatu i te tapeke 32.

$$a=-7 b=39$$

Tuhia anō te x^{2}+32x-273 hei \left(x^{2}-7x\right)+\left(39x-273\right).

$$\left(x^{2}-7x\right)+\left(39x-273\right)$$

Tauwehea te x i te tuatahi me te 39 i te rōpū tuarua.

$$x\left(x-7\right)+39\left(x-7\right)$$

Whakatauwehea atu te kīanga pātahi x-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-7\right)\left(x+39\right)$$

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.

$$x^{2}+32x-273=0$$

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.

$$x=\frac{-32±\sqrt{32^{2}-4\left(-273\right)}}{2}$$

Pūrua 32.

$$x=\frac{-32±\sqrt{1024-4\left(-273\right)}}{2}$$

Whakareatia -4 ki te -273.

$$x=\frac{-32±\sqrt{1024+1092}}{2}$$

Tāpiri 1024 ki te 1092.

$$x=\frac{-32±\sqrt{2116}}{2}$$

Tuhia te pūtakerua o te 2116.

$$x=\frac{-32±46}{2}$$

Nā, me whakaoti te whārite x=\frac{-32±46}{2} ina he tāpiri te ±. Tāpiri -32 ki te 46.

$$x=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$x=7$$

Nā, me whakaoti te whārite x=\frac{-32±46}{2} ina he tango te ±. Tango 46 mai i -32.

$$x=-\frac{78}{2}$$

Whakawehe -78 ki te 2.

$$x=-39$$

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 7 mō te x_{1} me te -39 mō te x_{2}.

$$x^{2}+32x-273=\left(x-7\right)\left(x-\left(-39\right)\right)$$

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

$$x^{2}+32x-273=\left(x-7\right)\left(x+39\right)$$

Aromātai

$$\left(x-7\right)\left(x+39\right)$$