Whakaoti i te x^2+12x+36=0

$$x ^ { 2 } + 12 x + 36 = 0$$

Whakaoti mō x

$$x=-6$$

Ngā Upane Whakamahi Tauwehe

Hei whakaoti i te whārite, whakatauwehea te x^{2}+12x+36 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=12 ab=36$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 36.

$$1,36 2,18 3,12 4,9 6,6$$

Tātaihia te tapeke mō ia takirua.

$$1+36=37 2+18=20 3+12=15 4+9=13 6+6=12$$

Ko te otinga te takirua ka hoatu i te tapeke 12.

$$a=6 b=6$$

Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.

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

Tuhia anōtia hei pūrua huarua.

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

Hei kimi i te otinga whārite, whakaotia te x+6=0.

$$x=-6$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=12 ab=1\times 36=36$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 36.

$$1,36 2,18 3,12 4,9 6,6$$

Tātaihia te tapeke mō ia takirua.

$$1+36=37 2+18=20 3+12=15 4+9=13 6+6=12$$

Ko te otinga te takirua ka hoatu i te tapeke 12.

$$a=6 b=6$$

Tuhia anō te x^{2}+12x+36 hei \left(x^{2}+6x\right)+\left(6x+36\right).

$$\left(x^{2}+6x\right)+\left(6x+36\right)$$

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

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

Whakatauwehea atu te kīanga pātahi x+6 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Tuhia anōtia hei pūrua huarua.

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

Hei kimi i te otinga whārite, whakaotia te x+6=0.

$$x=-6$$

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.

$$x^{2}+12x+36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 12 mō b, me 36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\times 36}}{2}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 36}}{2}$$

Whakareatia -4 ki te 36.

$$x=\frac{-12±\sqrt{144-144}}{2}$$

Tāpiri 144 ki te -144.

$$x=\frac{-12±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{12}{2}$$

Whakawehe -12 ki te 2.

$$x=-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Tauwehea te x^{2}+12x+36. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+6\right)^{2}=0$$

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

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x+6=0 x+6=0$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$x=-6 x=-6$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=-6$$