Whakaoti i te (x+2)^2=16

$$( x + 2 ) ^ { 2 } = 16$$

Whakaoti mō x

$$x=2$$

$$x=-6$$

Ngā Upane Whakamahi Tauwehe

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

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

Tangohia te 16 mai i ngā taha e rua.

$$x^{2}+4x+4-16=0$$

Tangohia te 16 i te 4, ka -12.

$$x^{2}+4x-12=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+4x-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.

$$a+b=4 ab=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. 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.

$$-1+12=11 -2+6=4 -3+4=1$$

Ko te otinga te takirua ka hoatu i te tapeke 4.

$$a=-2 b=6$$

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

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

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

Tangohia te 16 mai i ngā taha e rua.

$$x^{2}+4x+4-16=0$$

Tangohia te 16 i te 4, ka -12.

$$x^{2}+4x-12=0$$

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.

$$a+b=4 ab=1\left(-12\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. 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.

$$-1+12=11 -2+6=4 -3+4=1$$

Ko te otinga te takirua ka hoatu i te tapeke 4.

$$a=-2 b=6$$

Tuhia anō te x^{2}+4x-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

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

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

Tangohia te 16 mai i ngā taha e rua.

$$x^{2}+4x+4-16=0$$

Tangohia te 16 i te 4, ka -12.

$$x^{2}+4x-12=0$$

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

$$x=\frac{-4±\sqrt{4^{2}-4\left(-12\right)}}{2}$$

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\left(-12\right)}}{2}$$

Whakareatia -4 ki te -12.

$$x=\frac{-4±\sqrt{16+48}}{2}$$

Tāpiri 16 ki te 48.

$$x=\frac{-4±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{-4±8}{2}$$

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

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

Whakawehe 4 ki te 2.

$$x=2$$

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

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

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

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

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

Whakarūnātia.

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

Me tango 2 mai i ngā taha e rua o te whārite.

$$x=2 x=-6$$