Whakaoti i te -x^2-6x-9=

$$- x ^ { 2 } - 6 x - 9 =$$

Tauwehe

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

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx-9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-6 ab=-\left(-9\right)=9$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 9.

$$-1,-9 -3,-3$$

Tātaihia te tapeke mō ia takirua.

$$-1-9=-10 -3-3=-6$$

Ko te otinga te takirua ka hoatu i te tapeke -6.

$$a=-3 b=-3$$

Tuhia anō te -x^{2}-6x-9 hei \left(-x^{2}-3x\right)+\left(-3x-9\right).

$$\left(-x^{2}-3x\right)+\left(-3x-9\right)$$

Tauwehea te -x i te tuatahi me te -3 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi x+3 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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.

$$-x^{2}-6x-9=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-6\right)±\sqrt{36+4\left(-9\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -9.

$$x=\frac{-\left(-6\right)±\sqrt{36-36}}{2\left(-1\right)}$$

Tāpiri 36 ki te -36.

$$x=\frac{-\left(-6\right)±\sqrt{0}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 0.

$$x=\frac{-\left(-6\right)±0}{2\left(-1\right)}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±0}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{6±0}{-2}$$

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 -3 mō te x_{1} me te -3 mō te x_{2}.

$$-x^{2}-6x-9=-\left(x-\left(-3\right)\right)\left(x-\left(-3\right)\right)$$

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

$$-x^{2}-6x-9=-\left(x+3\right)\left(x+3\right)$$

Aromātai

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