Whakaoti i te 16x-16=x^2+8x

$$16 x - 16 = x ^ { 2 } + 8 x$$

Whakaoti mō x

$$x=4$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te x^{2} mai i ngā taha e rua.

$$16x-16-x^{2}=8x$$

Tangohia te 8x mai i ngā taha e rua.

$$16x-16-x^{2}-8x=0$$

Pahekotia te 16x me -8x, ka 8x.

$$8x-16-x^{2}=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-x^{2}+8x-16=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-16. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=-\left(-16\right)=16$$

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 16.

$$1,16 2,8 4,4$$

Tātaihia te tapeke mō ia takirua.

$$1+16=17 2+8=10 4+4=8$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=4 b=4$$

Tuhia anō te -x^{2}+8x-16 hei \left(-x^{2}+4x\right)+\left(4x-16\right).

$$\left(-x^{2}+4x\right)+\left(4x-16\right)$$

Tauwehea te -x i te tuatahi me te 4 i te rōpū tuarua.

$$-x\left(x-4\right)+4\left(x-4\right)$$

Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-4\right)\left(-x+4\right)$$

Hei kimi otinga whārite, me whakaoti te x-4=0 me te -x+4=0.

$$x=4 x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$16x-16-x^{2}=8x$$

Tangohia te 8x mai i ngā taha e rua.

$$16x-16-x^{2}-8x=0$$

Pahekotia te 16x me -8x, ka 8x.

$$8x-16-x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-x^{2}+8x-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 8 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-1\right)\left(-16\right)}}{2\left(-1\right)}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-1\right)\left(-16\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-8±\sqrt{64+4\left(-16\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -16.

$$x=\frac{-8±\sqrt{64-64}}{2\left(-1\right)}$$

Tāpiri 64 ki te -64.

$$x=\frac{-8±\sqrt{0}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{8}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=-\frac{8}{-2}$$

Whakawehe -8 ki te -2.

$$x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$16x-16-x^{2}=8x$$

Tangohia te 8x mai i ngā taha e rua.

$$16x-16-x^{2}-8x=0$$

Pahekotia te 16x me -8x, ka 8x.

$$8x-16-x^{2}=0$$

Me tāpiri te 16 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$8x-x^{2}=16$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-x^{2}+8x=16$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+8x}{-1}=\frac{16}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{8}{-1}x=\frac{16}{-1}$$

Whakawehe 8 ki te -1.

$$x^{2}-8x=\frac{16}{-1}$$

Whakawehe 16 ki te -1.

$$x^{2}-8x=-16$$

Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-8x+\left(-4\right)^{2}=-16+\left(-4\right)^{2}$$

Pūrua -4.

$$x^{2}-8x+16=-16+16$$

Tāpiri -16 ki te 16.

$$x^{2}-8x+16=0$$

Tauwehea x^{2}-8x+16. 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}.

$$\left(x-4\right)^{2}=0$$

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

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x-4=0 x-4=0$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=4 x=4$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=4$$