Whakaoti i te 8x=-4-4x^2

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

Whakaoti mō x

$$x=-1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te -4 mai i ngā taha e rua.

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

Ko te tauaro o -4 ko 4.

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

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$8x+4+4x^{2}=0$$

Whakawehea ngā taha e rua ki te 4.

$$2x+1+x^{2}=0$$

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

$$x^{2}+2x+1=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=1\times 1=1$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=1$$

Tuhia anō te x^{2}+2x+1 hei \left(x^{2}+x\right)+\left(x+1\right).

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

Whakatauwehea atu x i te x^{2}+x.

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

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

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

Tuhia anōtia hei pūrua huarua.

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

Hei kimi i te otinga whārite, whakaotia te x+1=0.

$$x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te -4 mai i ngā taha e rua.

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

Ko te tauaro o -4 ko 4.

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

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$8x+4+4x^{2}=0$$

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.

$$4x^{2}+8x+4=0$$

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

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

Pūrua 8.

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

Whakareatia -4 ki te 4.

$$x=\frac{-8±\sqrt{64-16\times 4}}{2\times 4}$$

Whakareatia -16 ki te 4.

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

Tāpiri 64 ki te -64.

$$x=\frac{-8±\sqrt{0}}{2\times 4}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{8}{2\times 4}$$

Whakareatia 2 ki te 4.

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

Whakawehe -8 ki te 8.

$$x=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 4x^{2} ki ngā taha e rua.

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

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.

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

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+8x}{4}=-\frac{4}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}+\frac{8}{4}x=-\frac{4}{4}$$

Whakawehe 8 ki te 4.

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

Whakawehe -4 ki te 4.

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

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.

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

Pūrua 1.

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

Tāpiri -1 ki te 1.

$$x^{2}+2x+1=0$$

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}.

$$\left(x+1\right)^{2}=0$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x+1=0 x+1=0$$

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

$$x=-1 x=-1$$

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

$$x=-1$$