Whakaoti i te (a+12)(a-4)=2a(a-4)

$$( a + 12 ) ( a - 4 ) = 2 a ( a - 4 )$$

Whakaoti mō a

$$a=12$$

$$a=4$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te āhuatanga tuaritanga hei whakarea te a+12 ki te a-4 ka whakakotahi i ngā kupu rite.

$$a^{2}+8a-48=2a\left(a-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2a ki te a-4.

$$a^{2}+8a-48=2a^{2}-8a$$

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

$$a^{2}+8a-48-2a^{2}=-8a$$

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

$$-a^{2}+8a-48=-8a$$

Me tāpiri te 8a ki ngā taha e rua.

$$-a^{2}+8a-48+8a=0$$

Pahekotia te 8a me 8a, ka 16a.

$$-a^{2}+16a-48=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -a^{2}+aa+ba-48. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=16 ab=-\left(-48\right)=48$$

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 48.

$$1,48 2,24 3,16 4,12 6,8$$

Tātaihia te tapeke mō ia takirua.

$$1+48=49 2+24=26 3+16=19 4+12=16 6+8=14$$

Ko te otinga te takirua ka hoatu i te tapeke 16.

$$a=12 b=4$$

Tuhia anō te -a^{2}+16a-48 hei \left(-a^{2}+12a\right)+\left(4a-48\right).

$$\left(-a^{2}+12a\right)+\left(4a-48\right)$$

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

$$-a\left(a-12\right)+4\left(a-12\right)$$

Whakatauwehea atu te kīanga pātahi a-12 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-12\right)\left(-a+4\right)$$

Hei kimi otinga whārite, me whakaoti te a-12=0 me te -a+4=0.

$$a=12 a=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te a+12 ki te a-4 ka whakakotahi i ngā kupu rite.

$$a^{2}+8a-48=2a\left(a-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2a ki te a-4.

$$a^{2}+8a-48=2a^{2}-8a$$

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

$$a^{2}+8a-48-2a^{2}=-8a$$

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

$$-a^{2}+8a-48=-8a$$

Me tāpiri te 8a ki ngā taha e rua.

$$-a^{2}+8a-48+8a=0$$

Pahekotia te 8a me 8a, ka 16a.

$$-a^{2}+16a-48=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 16 mō b, me -48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-16±\sqrt{16^{2}-4\left(-1\right)\left(-48\right)}}{2\left(-1\right)}$$

Pūrua 16.

$$a=\frac{-16±\sqrt{256-4\left(-1\right)\left(-48\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$a=\frac{-16±\sqrt{256+4\left(-48\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -48.

$$a=\frac{-16±\sqrt{256-192}}{2\left(-1\right)}$$

Tāpiri 256 ki te -192.

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

Tuhia te pūtakerua o te 64.

$$a=\frac{-16±8}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$a=\frac{-16±8}{-2}$$

Nā, me whakaoti te whārite a=\frac{-16±8}{-2} ina he tāpiri te ±. Tāpiri -16 ki te 8.

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

Whakawehe -8 ki te -2.

$$a=4$$

Nā, me whakaoti te whārite a=\frac{-16±8}{-2} ina he tango te ±. Tango 8 mai i -16.

$$a=-\frac{24}{-2}$$

Whakawehe -24 ki te -2.

$$a=12$$

Kua oti te whārite te whakatau.

$$a=4 a=12$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te a+12 ki te a-4 ka whakakotahi i ngā kupu rite.

$$a^{2}+8a-48=2a\left(a-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2a ki te a-4.

$$a^{2}+8a-48=2a^{2}-8a$$

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

$$a^{2}+8a-48-2a^{2}=-8a$$

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

$$-a^{2}+8a-48=-8a$$

Me tāpiri te 8a ki ngā taha e rua.

$$-a^{2}+8a-48+8a=0$$

Pahekotia te 8a me 8a, ka 16a.

$$-a^{2}+16a-48=0$$

Me tāpiri te 48 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-a^{2}+16a=48$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-a^{2}+16a}{-1}=\frac{48}{-1}$$

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

$$a^{2}+\frac{16}{-1}a=\frac{48}{-1}$$

Whakawehe 16 ki te -1.

$$a^{2}-16a=\frac{48}{-1}$$

Whakawehe 48 ki te -1.

$$a^{2}-16a=-48$$

Whakawehea te -16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -8. Nā, tāpiria te pūrua o te -8 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}-16a+\left(-8\right)^{2}=-48+\left(-8\right)^{2}$$

Pūrua -8.

$$a^{2}-16a+64=-48+64$$

Tāpiri -48 ki te 64.

$$a^{2}-16a+64=16$$

Tauwehea a^{2}-16a+64. 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}.

$$\left(a-8\right)^{2}=16$$

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

$$\sqrt{\left(a-8\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$a-8=4 a-8=-4$$

Me tāpiri 8 ki ngā taha e rua o te whārite.

$$a=12 a=4$$