Whakaoti i te -3x^2-6x+9=0

$$- 3 x ^ { 2 } - 6 x + 9 = 0$$

Whakaoti mō x

$$x=-3$$

$$x=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakawehea ngā taha e rua ki te 3.

$$-x^{2}-2x+3=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=-3=-3$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=-3$$

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

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

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

$$x\left(-x+1\right)+3\left(-x+1\right)$$

Whakatauwehea atu te kīanga pātahi -x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x+1\right)\left(x+3\right)$$

Hei kimi otinga whārite, me whakaoti te -x+1=0 me te x+3=0.

$$x=1 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$-3x^{2}-6x+9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, -6 mō b, me 9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-3\right)\times 9}}{2\left(-3\right)}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-3\right)\times 9}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-\left(-6\right)±\sqrt{36+12\times 9}}{2\left(-3\right)}$$

Whakareatia 12 ki te 9.

$$x=\frac{-\left(-6\right)±\sqrt{36+108}}{2\left(-3\right)}$$

Tāpiri 36 ki te 108.

$$x=\frac{-\left(-6\right)±\sqrt{144}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{-\left(-6\right)±12}{2\left(-3\right)}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±12}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{6±12}{-6}$$

Nā, me whakaoti te whārite x=\frac{6±12}{-6} ina he tāpiri te ±. Tāpiri 6 ki te 12.

$$x=\frac{18}{-6}$$

Whakawehe 18 ki te -6.

$$x=-3$$

Nā, me whakaoti te whārite x=\frac{6±12}{-6} ina he tango te ±. Tango 12 mai i 6.

$$x=-\frac{6}{-6}$$

Whakawehe -6 ki te -6.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=-3 x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-3x^{2}-6x+9=0$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$-3x^{2}-6x+9-9=-9$$

Mā te tango i te 9 i a ia ake anō ka toe ko te 0.

$$-3x^{2}-6x=-9$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}-6x}{-3}=-\frac{9}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

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

Whakawehe -6 ki te -3.

$$x^{2}+2x=-\frac{9}{-3}$$

Whakawehe -9 ki te -3.

$$x^{2}+2x=3$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+2x+1^{2}=3+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=3+1$$

Tāpiri 3 ki te 1.

$$x^{2}+2x+1=4$$

Tauwehea x^{2}+2x+1. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=4$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{4}$$

Whakarūnātia.

$$x+1=2 x+1=-2$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=1 x=-3$$