Whakaoti i te (x+6)^2-16=0

$$( x + 6 ) ^ { 2 } - 16 = 0$$

Whakaoti mō x

$$x=-2$$

$$x=-10$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+6\right)^{2}.

$$x^{2}+12x+36-16=0$$

Tangohia te 16 i te 36, ka 20.

$$x^{2}+12x+20=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+12x+20 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.

$$a+b=12 ab=20$$

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 20.

$$1,20 2,10 4,5$$

Tātaihia te tapeke mō ia takirua.

$$1+20=21 2+10=12 4+5=9$$

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

$$a=2 b=10$$

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

$$\left(x+2\right)\left(x+10\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+10=0.

$$x=-2 x=-10$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+6\right)^{2}.

$$x^{2}+12x+36-16=0$$

Tangohia te 16 i te 36, ka 20.

$$x^{2}+12x+20=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+20. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=12 ab=1\times 20=20$$

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 20.

$$1,20 2,10 4,5$$

Tātaihia te tapeke mō ia takirua.

$$1+20=21 2+10=12 4+5=9$$

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

$$a=2 b=10$$

Tuhia anō te x^{2}+12x+20 hei \left(x^{2}+2x\right)+\left(10x+20\right).

$$\left(x^{2}+2x\right)+\left(10x+20\right)$$

Tauwehea te x i te tuatahi me te 10 i te rōpū tuarua.

$$x\left(x+2\right)+10\left(x+2\right)$$

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

$$\left(x+2\right)\left(x+10\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+10=0.

$$x=-2 x=-10$$

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(x+6\right)^{2}.

$$x^{2}+12x+36-16=0$$

Tangohia te 16 i te 36, ka 20.

$$x^{2}+12x+20=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 12 mō b, me 20 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\times 20}}{2}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 20}}{2}$$

Whakareatia -4 ki te 20.

$$x=\frac{-12±\sqrt{144-80}}{2}$$

Tāpiri 144 ki te -80.

$$x=\frac{-12±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{-12±8}{2}$$

Nā, me whakaoti te whārite x=\frac{-12±8}{2} ina he tāpiri te ±. Tāpiri -12 ki te 8.

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

Whakawehe -4 ki te 2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-12±8}{2} ina he tango te ±. Tango 8 mai i -12.

$$x=-\frac{20}{2}$$

Whakawehe -20 ki te 2.

$$x=-10$$

Kua oti te whārite te whakatau.

$$x=-2 x=-10$$

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(x+6\right)^{2}.

$$x^{2}+12x+36-16=0$$

Tangohia te 16 i te 36, ka 20.

$$x^{2}+12x+20=0$$

Tangohia te 20 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+12x=-20$$

Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+12x+6^{2}=-20+6^{2}$$

Pūrua 6.

$$x^{2}+12x+36=-20+36$$

Tāpiri -20 ki te 36.

$$x^{2}+12x+36=16$$

Tauwehea x^{2}+12x+36. 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}.

$$\left(x+6\right)^{2}=16$$

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

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x+6=4 x+6=-4$$

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

$$x=-2 x=-10$$