Whakaoti i te (x-6)^2=144

$$( x - 6 ) ^ { 2 } = 144$$

Whakaoti mō x

$$x=18$$

$$x=-6$$

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}.

$$x^{2}-12x+36=144$$

Tangohia te 144 mai i ngā taha e rua.

$$x^{2}-12x+36-144=0$$

Tangohia te 144 i te 36, ka -108.

$$x^{2}-12x-108=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}-12x-108 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.

$$a+b=-12 ab=-108$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -108.

$$1,-108 2,-54 3,-36 4,-27 6,-18 9,-12$$

Tātaihia te tapeke mō ia takirua.

$$1-108=-107 2-54=-52 3-36=-33 4-27=-23 6-18=-12 9-12=-3$$

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

$$a=-18 b=6$$

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

$$\left(x-18\right)\left(x+6\right)$$

Hei kimi otinga whārite, me whakaoti te x-18=0 me te x+6=0.

$$x=18 x=-6$$

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-6\right)^{2}.

$$x^{2}-12x+36=144$$

Tangohia te 144 mai i ngā taha e rua.

$$x^{2}-12x+36-144=0$$

Tangohia te 144 i te 36, ka -108.

$$x^{2}-12x-108=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-108. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-12 ab=1\left(-108\right)=-108$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -108.

$$1,-108 2,-54 3,-36 4,-27 6,-18 9,-12$$

Tātaihia te tapeke mō ia takirua.

$$1-108=-107 2-54=-52 3-36=-33 4-27=-23 6-18=-12 9-12=-3$$

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

$$a=-18 b=6$$

Tuhia anō te x^{2}-12x-108 hei \left(x^{2}-18x\right)+\left(6x-108\right).

$$\left(x^{2}-18x\right)+\left(6x-108\right)$$

Tauwehea te x i te tuatahi me te 6 i te rōpū tuarua.

$$x\left(x-18\right)+6\left(x-18\right)$$

Whakatauwehea atu te kīanga pātahi x-18 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-18\right)\left(x+6\right)$$

Hei kimi otinga whārite, me whakaoti te x-18=0 me te x+6=0.

$$x=18 x=-6$$

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-6\right)^{2}.

$$x^{2}-12x+36=144$$

Tangohia te 144 mai i ngā taha e rua.

$$x^{2}-12x+36-144=0$$

Tangohia te 144 i te 36, ka -108.

$$x^{2}-12x-108=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -12 mō b, me -108 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-108\right)}}{2}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-108\right)}}{2}$$

Whakareatia -4 ki te -108.

$$x=\frac{-\left(-12\right)±\sqrt{144+432}}{2}$$

Tāpiri 144 ki te 432.

$$x=\frac{-\left(-12\right)±\sqrt{576}}{2}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{-\left(-12\right)±24}{2}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±24}{2}$$

Nā, me whakaoti te whārite x=\frac{12±24}{2} ina he tāpiri te ±. Tāpiri 12 ki te 24.

$$x=\frac{36}{2}$$

Whakawehe 36 ki te 2.

$$x=18$$

Nā, me whakaoti te whārite x=\frac{12±24}{2} ina he tango te ±. Tango 24 mai i 12.

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

Whakawehe -12 ki te 2.

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=18 x=-6$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{144}$$

Whakarūnātia.

$$x-6=12 x-6=-12$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$x=18 x=-6$$