Whakaoti i te left(-2x-8right)^2=-8x

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

Whakaoti mō x

$$x=-8$$

$$x=-2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-2x-8\right)^{2}.

$$4x^{2}+32x+64=-8x$$

Me tāpiri te 8x ki ngā taha e rua.

$$4x^{2}+32x+64+8x=0$$

Pahekotia te 32x me 8x, ka 40x.

$$4x^{2}+40x+64=0$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}+10x+16=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+16. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=10 ab=1\times 16=16$$

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 16.

$$1,16 2,8 4,4$$

Tātaihia te tapeke mō ia takirua.

$$1+16=17 2+8=10 4+4=8$$

Ko te otinga te takirua ka hoatu i te tapeke 10.

$$a=2 b=8$$

Tuhia anō te x^{2}+10x+16 hei \left(x^{2}+2x\right)+\left(8x+16\right).

$$\left(x^{2}+2x\right)+\left(8x+16\right)$$

Tauwehea te x i te tuatahi me te 8 i te rōpū tuarua.

$$x\left(x+2\right)+8\left(x+2\right)$$

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

$$\left(x+2\right)\left(x+8\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+8=0.

$$x=-2 x=-8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-2x-8\right)^{2}.

$$4x^{2}+32x+64=-8x$$

Me tāpiri te 8x ki ngā taha e rua.

$$4x^{2}+32x+64+8x=0$$

Pahekotia te 32x me 8x, ka 40x.

$$4x^{2}+40x+64=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 40 mō b, me 64 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-40±\sqrt{40^{2}-4\times 4\times 64}}{2\times 4}$$

Pūrua 40.

$$x=\frac{-40±\sqrt{1600-4\times 4\times 64}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-40±\sqrt{1600-16\times 64}}{2\times 4}$$

Whakareatia -16 ki te 64.

$$x=\frac{-40±\sqrt{1600-1024}}{2\times 4}$$

Tāpiri 1600 ki te -1024.

$$x=\frac{-40±\sqrt{576}}{2\times 4}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{-40±24}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-40±24}{8}$$

Nā, me whakaoti te whārite x=\frac{-40±24}{8} ina he tāpiri te ±. Tāpiri -40 ki te 24.

$$x=-\frac{16}{8}$$

Whakawehe -16 ki te 8.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-40±24}{8} ina he tango te ±. Tango 24 mai i -40.

$$x=-\frac{64}{8}$$

Whakawehe -64 ki te 8.

$$x=-8$$

Kua oti te whārite te whakatau.

$$x=-2 x=-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-2x-8\right)^{2}.

$$4x^{2}+32x+64=-8x$$

Me tāpiri te 8x ki ngā taha e rua.

$$4x^{2}+32x+64+8x=0$$

Pahekotia te 32x me 8x, ka 40x.

$$4x^{2}+40x+64=0$$

Tangohia te 64 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$4x^{2}+40x=-64$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+40x}{4}=-\frac{64}{4}$$

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

$$x^{2}+\frac{40}{4}x=-\frac{64}{4}$$

Whakawehe 40 ki te 4.

$$x^{2}+10x=-\frac{64}{4}$$

Whakawehe -64 ki te 4.

$$x^{2}+10x=-16$$

Whakawehea te 10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 5. Nā, tāpiria te pūrua o te 5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+10x+5^{2}=-16+5^{2}$$

Pūrua 5.

$$x^{2}+10x+25=-16+25$$

Tāpiri -16 ki te 25.

$$x^{2}+10x+25=9$$

Tauwehea x^{2}+10x+25. 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}.

$$\left(x+5\right)^{2}=9$$

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

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$x+5=3 x+5=-3$$

Me tango 5 mai i ngā taha e rua o te whārite.

$$x=-2 x=-8$$