Whakaoti i te (x-7)^2=16

$$( x - 7 ) ^ { 2 } = 16$$

Whakaoti mō x

$$x=11$$

$$x=3$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-7\right)^{2}.

$$x^{2}-14x+49=16$$

Tangohia te 16 mai i ngā taha e rua.

$$x^{2}-14x+49-16=0$$

Tangohia te 16 i te 49, ka 33.

$$x^{2}-14x+33=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}-14x+33 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.

$$a+b=-14 ab=33$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 33.

$$-1,-33 -3,-11$$

Tātaihia te tapeke mō ia takirua.

$$-1-33=-34 -3-11=-14$$

Ko te otinga te takirua ka hoatu i te tapeke -14.

$$a=-11 b=-3$$

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

$$\left(x-11\right)\left(x-3\right)$$

Hei kimi otinga whārite, me whakaoti te x-11=0 me te x-3=0.

$$x=11 x=3$$

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-7\right)^{2}.

$$x^{2}-14x+49=16$$

Tangohia te 16 mai i ngā taha e rua.

$$x^{2}-14x+49-16=0$$

Tangohia te 16 i te 49, ka 33.

$$x^{2}-14x+33=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+33. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-14 ab=1\times 33=33$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 33.

$$-1,-33 -3,-11$$

Tātaihia te tapeke mō ia takirua.

$$-1-33=-34 -3-11=-14$$

Ko te otinga te takirua ka hoatu i te tapeke -14.

$$a=-11 b=-3$$

Tuhia anō te x^{2}-14x+33 hei \left(x^{2}-11x\right)+\left(-3x+33\right).

$$\left(x^{2}-11x\right)+\left(-3x+33\right)$$

Tauwehea te x i te tuatahi me te -3 i te rōpū tuarua.

$$x\left(x-11\right)-3\left(x-11\right)$$

Whakatauwehea atu te kīanga pātahi x-11 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-11\right)\left(x-3\right)$$

Hei kimi otinga whārite, me whakaoti te x-11=0 me te x-3=0.

$$x=11 x=3$$

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-7\right)^{2}.

$$x^{2}-14x+49=16$$

Tangohia te 16 mai i ngā taha e rua.

$$x^{2}-14x+49-16=0$$

Tangohia te 16 i te 49, ka 33.

$$x^{2}-14x+33=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -14 mō b, me 33 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 33}}{2}$$

Pūrua -14.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\times 33}}{2}$$

Whakareatia -4 ki te 33.

$$x=\frac{-\left(-14\right)±\sqrt{196-132}}{2}$$

Tāpiri 196 ki te -132.

$$x=\frac{-\left(-14\right)±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{-\left(-14\right)±8}{2}$$

Ko te tauaro o -14 ko 14.

$$x=\frac{14±8}{2}$$

Nā, me whakaoti te whārite x=\frac{14±8}{2} ina he tāpiri te ±. Tāpiri 14 ki te 8.

$$x=\frac{22}{2}$$

Whakawehe 22 ki te 2.

$$x=11$$

Nā, me whakaoti te whārite x=\frac{14±8}{2} ina he tango te ±. Tango 8 mai i 14.

$$x=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$x=3$$

Kua oti te whārite te whakatau.

$$x=11 x=3$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$\sqrt{\left(x-7\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x-7=4 x-7=-4$$

Me tāpiri 7 ki ngā taha e rua o te whārite.

$$x=11 x=3$$