Whakaoti i te x^2+12=-8x

$$x ^ { 2 } + 12 = - 8 x$$

Whakaoti mō x

$$x=-6$$

$$x=-2$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 8x ki ngā taha e rua.

$$x^{2}+12+8x=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$x^{2}+8x+12=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+8x+12 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.

$$a+b=8 ab=12$$

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 12.

$$1,12 2,6 3,4$$

Tātaihia te tapeke mō ia takirua.

$$1+12=13 2+6=8 3+4=7$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=2 b=6$$

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

$$\left(x+2\right)\left(x+6\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+6=0.

$$x=-2 x=-6$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Me tāpiri te 8x ki ngā taha e rua.

$$x^{2}+12+8x=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$x^{2}+8x+12=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=1\times 12=12$$

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 12.

$$1,12 2,6 3,4$$

Tātaihia te tapeke mō ia takirua.

$$1+12=13 2+6=8 3+4=7$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=2 b=6$$

Tuhia anō te x^{2}+8x+12 hei \left(x^{2}+2x\right)+\left(6x+12\right).

$$\left(x^{2}+2x\right)+\left(6x+12\right)$$

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

$$x\left(x+2\right)+6\left(x+2\right)$$

Whakatauwehea atu te kīanga pātahi x+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x+2\right)\left(x+6\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+6=0.

$$x=-2 x=-6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 8x ki ngā taha e rua.

$$x^{2}+12+8x=0$$

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.

$$x^{2}+8x+12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me 12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 12}}{2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 12}}{2}$$

Whakareatia -4 ki te 12.

$$x=\frac{-8±\sqrt{64-48}}{2}$$

Tāpiri 64 ki te -48.

$$x=\frac{-8±\sqrt{16}}{2}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{-8±4}{2}$$

Nā, me whakaoti te whārite x=\frac{-8±4}{2} ina he tāpiri te ±. Tāpiri -8 ki te 4.

$$x=-\frac{4}{2}$$

Whakawehe -4 ki te 2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-8±4}{2} ina he tango te ±. Tango 4 mai i -8.

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

Whakawehe -12 ki te 2.

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=-2 x=-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 8x ki ngā taha e rua.

$$x^{2}+12+8x=0$$

Tangohia te 12 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+8x=-12$$

Whakawehea te 8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 4. Nā, tāpiria te pūrua o te 4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+8x+4^{2}=-12+4^{2}$$

Pūrua 4.

$$x^{2}+8x+16=-12+16$$

Tāpiri -12 ki te 16.

$$x^{2}+8x+16=4$$

Tauwehea x^{2}+8x+16. 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}.

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

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

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

Whakarūnātia.

$$x+4=2 x+4=-2$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$x=-2 x=-6$$