Whakaoti i te q^2+4q+4-2q^2=8

$$q ^ { 2 } + 4 q + 4 - 2 q ^ { 2 } = 8$$

Whakaoti mō q

$$q=2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Pahekotia te q^{2} me -2q^{2}, ka -q^{2}.

$$-q^{2}+4q+4=8$$

Tangohia te 8 mai i ngā taha e rua.

$$-q^{2}+4q+4-8=0$$

Tangohia te 8 i te 4, ka -4.

$$-q^{2}+4q-4=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -q^{2}+aq+bq-4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=4 ab=-\left(-4\right)=4$$

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 4.

$$1,4 2,2$$

Tātaihia te tapeke mō ia takirua.

$$1+4=5 2+2=4$$

Ko te otinga te takirua ka hoatu i te tapeke 4.

$$a=2 b=2$$

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

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

Tauwehea te -q i te tuatahi me te 2 i te rōpū tuarua.

$$-q\left(q-2\right)+2\left(q-2\right)$$

Whakatauwehea atu te kīanga pātahi q-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(q-2\right)\left(-q+2\right)$$

Hei kimi otinga whārite, me whakaoti te q-2=0 me te -q+2=0.

$$q=2 q=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te q^{2} me -2q^{2}, ka -q^{2}.

$$-q^{2}+4q+4=8$$

Tangohia te 8 mai i ngā taha e rua.

$$-q^{2}+4q+4-8=0$$

Tangohia te 8 i te 4, ka -4.

$$-q^{2}+4q-4=0$$

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

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

Pūrua 4.

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

Whakareatia -4 ki te -1.

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

Whakareatia 4 ki te -4.

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

Tāpiri 16 ki te -16.

$$q=\frac{-4±\sqrt{0}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 0.

$$q=-\frac{4}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

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

Whakawehe -4 ki te -2.

$$q=2$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te q^{2} me -2q^{2}, ka -q^{2}.

$$-q^{2}+4q+4=8$$

Tangohia te 4 mai i ngā taha e rua.

$$-q^{2}+4q=8-4$$

Tangohia te 4 i te 8, ka 4.

$$-q^{2}+4q=4$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-q^{2}+4q}{-1}=\frac{4}{-1}$$

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

$$q^{2}+\frac{4}{-1}q=\frac{4}{-1}$$

Whakawehe 4 ki te -1.

$$q^{2}-4q=\frac{4}{-1}$$

Whakawehe 4 ki te -1.

$$q^{2}-4q=-4$$

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

$$q^{2}-4q+\left(-2\right)^{2}=-4+\left(-2\right)^{2}$$

Pūrua -2.

$$q^{2}-4q+4=-4+4$$

Tāpiri -4 ki te 4.

$$q^{2}-4q+4=0$$

Tauwehea q^{2}-4q+4. 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}.

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

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

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

Whakarūnātia.

$$q-2=0 q-2=0$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$q=2 q=2$$

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

$$q=2$$