Whakaoti i te xx+90x+176=0

$$xx+90x+176=0$$

Whakaoti mō x

$$x=-88$$

$$x=-2$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+90x+176=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+90x+176 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.

$$a+b=90 ab=176$$

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 176.

$$1,176 2,88 4,44 8,22 11,16$$

Tātaihia te tapeke mō ia takirua.

$$1+176=177 2+88=90 4+44=48 8+22=30 11+16=27$$

Ko te otinga te takirua ka hoatu i te tapeke 90.

$$a=2 b=88$$

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

$$\left(x+2\right)\left(x+88\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+88=0.

$$x=-2 x=-88$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+90x+176=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+176. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=90 ab=1\times 176=176$$

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 176.

$$1,176 2,88 4,44 8,22 11,16$$

Tātaihia te tapeke mō ia takirua.

$$1+176=177 2+88=90 4+44=48 8+22=30 11+16=27$$

Ko te otinga te takirua ka hoatu i te tapeke 90.

$$a=2 b=88$$

Tuhia anō te x^{2}+90x+176 hei \left(x^{2}+2x\right)+\left(88x+176\right).

$$\left(x^{2}+2x\right)+\left(88x+176\right)$$

Tauwehea te x i te tuatahi me te 88 i te rōpū tuarua.

$$x\left(x+2\right)+88\left(x+2\right)$$

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

$$\left(x+2\right)\left(x+88\right)$$

Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+88=0.

$$x=-2 x=-88$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+90x+176=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 90 mō b, me 176 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-90±\sqrt{90^{2}-4\times 176}}{2}$$

Pūrua 90.

$$x=\frac{-90±\sqrt{8100-4\times 176}}{2}$$

Whakareatia -4 ki te 176.

$$x=\frac{-90±\sqrt{8100-704}}{2}$$

Tāpiri 8100 ki te -704.

$$x=\frac{-90±\sqrt{7396}}{2}$$

Tuhia te pūtakerua o te 7396.

$$x=\frac{-90±86}{2}$$

Nā, me whakaoti te whārite x=\frac{-90±86}{2} ina he tāpiri te ±. Tāpiri -90 ki te 86.

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

Whakawehe -4 ki te 2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-90±86}{2} ina he tango te ±. Tango 86 mai i -90.

$$x=-\frac{176}{2}$$

Whakawehe -176 ki te 2.

$$x=-88$$

Kua oti te whārite te whakatau.

$$x=-2 x=-88$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+90x+176=0$$

Tangohia te 176 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+90x=-176$$

Whakawehea te 90, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 45. Nā, tāpiria te pūrua o te 45 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+90x+45^{2}=-176+45^{2}$$

Pūrua 45.

$$x^{2}+90x+2025=-176+2025$$

Tāpiri -176 ki te 2025.

$$x^{2}+90x+2025=1849$$

Tauwehea x^{2}+90x+2025. 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}.

$$\left(x+45\right)^{2}=1849$$

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

$$\sqrt{\left(x+45\right)^{2}}=\sqrt{1849}$$

Whakarūnātia.

$$x+45=43 x+45=-43$$

Me tango 45 mai i ngā taha e rua o te whārite.

$$x=-2 x=-88$$