Whakaoti i te 144=left(x+1right)^2

$$144= { \left(x+1 \right) }^{ 2 }$$

Whakaoti mō x

$$x=11$$

$$x=-13$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$144=x^{2}+2x+1$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}+2x+1=144$$

Tangohia te 144 mai i ngā taha e rua.

$$x^{2}+2x+1-144=0$$

Tangohia te 144 i te 1, ka -143.

$$x^{2}+2x-143=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+2x-143 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.

$$a+b=2 ab=-143$$

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 -143.

$$-1,143 -11,13$$

Tātaihia te tapeke mō ia takirua.

$$-1+143=142 -11+13=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=-11 b=13$$

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

$$\left(x-11\right)\left(x+13\right)$$

Hei kimi otinga whārite, me whakaoti te x-11=0 me te x+13=0.

$$x=11 x=-13$$

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+1\right)^{2}.

$$144=x^{2}+2x+1$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}+2x+1=144$$

Tangohia te 144 mai i ngā taha e rua.

$$x^{2}+2x+1-144=0$$

Tangohia te 144 i te 1, ka -143.

$$x^{2}+2x-143=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-143. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=1\left(-143\right)=-143$$

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 -143.

$$-1,143 -11,13$$

Tātaihia te tapeke mō ia takirua.

$$-1+143=142 -11+13=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=-11 b=13$$

Tuhia anō te x^{2}+2x-143 hei \left(x^{2}-11x\right)+\left(13x-143\right).

$$\left(x^{2}-11x\right)+\left(13x-143\right)$$

Tauwehea te x i te tuatahi me te 13 i te rōpū tuarua.

$$x\left(x-11\right)+13\left(x-11\right)$$

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

$$\left(x-11\right)\left(x+13\right)$$

Hei kimi otinga whārite, me whakaoti te x-11=0 me te x+13=0.

$$x=11 x=-13$$

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+1\right)^{2}.

$$144=x^{2}+2x+1$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}+2x+1=144$$

Tangohia te 144 mai i ngā taha e rua.

$$x^{2}+2x+1-144=0$$

Tangohia te 144 i te 1, ka -143.

$$x^{2}+2x-143=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -143 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-143\right)}}{2}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\left(-143\right)}}{2}$$

Whakareatia -4 ki te -143.

$$x=\frac{-2±\sqrt{4+572}}{2}$$

Tāpiri 4 ki te 572.

$$x=\frac{-2±\sqrt{576}}{2}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{-2±24}{2}$$

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

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

Whakawehe 22 ki te 2.

$$x=11$$

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

$$x=-\frac{26}{2}$$

Whakawehe -26 ki te 2.

$$x=-13$$

Kua oti te whārite te whakatau.

$$x=11 x=-13$$

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+1\right)^{2}.

$$144=x^{2}+2x+1$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}+2x+1=144$$

Tauwehea x^{2}+2x+1. 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}.

$$\left(x+1\right)^{2}=144$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{144}$$

Whakarūnātia.

$$x+1=12 x+1=-12$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=11 x=-13$$