Whakaoti i te x^2+8=-6x

$$x ^ { 2 } + 8 = - 6 x$$

Whakaoti mō x

$$x=-4$$

$$x=-2$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}+8+6x=0$$

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

$$x^{2}+6x+8=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+6x+8 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.

$$a+b=6 ab=8$$

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 8.

$$1,8 2,4$$

Tātaihia te tapeke mō ia takirua.

$$1+8=9 2+4=6$$

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

$$a=2 b=4$$

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

$$\left(x+2\right)\left(x+4\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+4=0.

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

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}+8+6x=0$$

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

$$x^{2}+6x+8=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+8. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=1\times 8=8$$

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 8.

$$1,8 2,4$$

Tātaihia te tapeke mō ia takirua.

$$1+8=9 2+4=6$$

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

$$a=2 b=4$$

Tuhia anō te x^{2}+6x+8 hei \left(x^{2}+2x\right)+\left(4x+8\right).

$$\left(x^{2}+2x\right)+\left(4x+8\right)$$

Tauwehea te x i te tuatahi me te 4 i te rōpū tuarua.

$$x\left(x+2\right)+4\left(x+2\right)$$

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

$$\left(x+2\right)\left(x+4\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+4=0.

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}+8+6x=0$$

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.

$$x^{2}+6x+8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\times 8}}{2}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\times 8}}{2}$$

Whakareatia -4 ki te 8.

$$x=\frac{-6±\sqrt{36-32}}{2}$$

Tāpiri 36 ki te -32.

$$x=\frac{-6±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{-6±2}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2.

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

Whakawehe -4 ki te 2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-6±2}{2} ina he tango te ±. Tango 2 mai i -6.

$$x=-\frac{8}{2}$$

Whakawehe -8 ki te 2.

$$x=-4$$

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}+8+6x=0$$

Tangohia te 8 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+6x=-8$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+6x+3^{2}=-8+3^{2}$$

Pūrua 3.

$$x^{2}+6x+9=-8+9$$

Tāpiri -8 ki te 9.

$$x^{2}+6x+9=1$$

Tauwehea x^{2}+6x+9. 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}.

$$\left(x+3\right)^{2}=1$$

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

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{1}$$

Whakarūnātia.

$$x+3=1 x+3=-1$$

Me tango 3 mai i ngā taha e rua o te whārite.

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