Whakaoti i te 16a^2+21a+9=6a^2

$$16 a ^ { 2 } + 21 a + 9 = 6 a ^ { 2 }$$

Whakaoti mō a

$$a=-\frac{3}{5}=-0.6$$

$$a = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 6a^{2} mai i ngā taha e rua.

$$16a^{2}+21a+9-6a^{2}=0$$

Pahekotia te 16a^{2} me -6a^{2}, ka 10a^{2}.

$$10a^{2}+21a+9=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 10a^{2}+aa+ba+9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=21 ab=10\times 9=90$$

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 90.

$$1,90 2,45 3,30 5,18 6,15 9,10$$

Tātaihia te tapeke mō ia takirua.

$$1+90=91 2+45=47 3+30=33 5+18=23 6+15=21 9+10=19$$

Ko te otinga te takirua ka hoatu i te tapeke 21.

$$a=6 b=15$$

Tuhia anō te 10a^{2}+21a+9 hei \left(10a^{2}+6a\right)+\left(15a+9\right).

$$\left(10a^{2}+6a\right)+\left(15a+9\right)$$

Tauwehea te 2a i te tuatahi me te 3 i te rōpū tuarua.

$$2a\left(5a+3\right)+3\left(5a+3\right)$$

Whakatauwehea atu te kīanga pātahi 5a+3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(5a+3\right)\left(2a+3\right)$$

Hei kimi otinga whārite, me whakaoti te 5a+3=0 me te 2a+3=0.

$$a=-\frac{3}{5} a=-\frac{3}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 6a^{2} mai i ngā taha e rua.

$$16a^{2}+21a+9-6a^{2}=0$$

Pahekotia te 16a^{2} me -6a^{2}, ka 10a^{2}.

$$10a^{2}+21a+9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 10 mō a, 21 mō b, me 9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-21±\sqrt{21^{2}-4\times 10\times 9}}{2\times 10}$$

Pūrua 21.

$$a=\frac{-21±\sqrt{441-4\times 10\times 9}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$a=\frac{-21±\sqrt{441-40\times 9}}{2\times 10}$$

Whakareatia -40 ki te 9.

$$a=\frac{-21±\sqrt{441-360}}{2\times 10}$$

Tāpiri 441 ki te -360.

$$a=\frac{-21±\sqrt{81}}{2\times 10}$$

Tuhia te pūtakerua o te 81.

$$a=\frac{-21±9}{2\times 10}$$

Whakareatia 2 ki te 10.

$$a=\frac{-21±9}{20}$$

Nā, me whakaoti te whārite a=\frac{-21±9}{20} ina he tāpiri te ±. Tāpiri -21 ki te 9.

$$a=-\frac{12}{20}$$

Whakahekea te hautanga \frac{-12}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$a=-\frac{3}{5}$$

Nā, me whakaoti te whārite a=\frac{-21±9}{20} ina he tango te ±. Tango 9 mai i -21.

$$a=-\frac{30}{20}$$

Whakahekea te hautanga \frac{-30}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$a=-\frac{3}{2}$$

Kua oti te whārite te whakatau.

$$a=-\frac{3}{5} a=-\frac{3}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 6a^{2} mai i ngā taha e rua.

$$16a^{2}+21a+9-6a^{2}=0$$

Pahekotia te 16a^{2} me -6a^{2}, ka 10a^{2}.

$$10a^{2}+21a+9=0$$

Tangohia te 9 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$10a^{2}+21a=-9$$

Whakawehea ngā taha e rua ki te 10.

$$\frac{10a^{2}+21a}{10}=-\frac{9}{10}$$

Mā te whakawehe ki te 10 ka wetekia te whakareanga ki te 10.

$$a^{2}+\frac{21}{10}a=-\frac{9}{10}$$

Whakawehea te \frac{21}{10}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{21}{20}. Nā, tāpiria te pūrua o te \frac{21}{20} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}+\frac{21}{10}a+\left(\frac{21}{20}\right)^{2}=-\frac{9}{10}+\left(\frac{21}{20}\right)^{2}$$

Pūruatia \frac{21}{20} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}+\frac{21}{10}a+\frac{441}{400}=-\frac{9}{10}+\frac{441}{400}$$

Tāpiri -\frac{9}{10} ki te \frac{441}{400} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$a^{2}+\frac{21}{10}a+\frac{441}{400}=\frac{81}{400}$$

Tauwehea te a^{2}+\frac{21}{10}a+\frac{441}{400}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(a+\frac{21}{20}\right)^{2}=\frac{81}{400}$$

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

$$\sqrt{\left(a+\frac{21}{20}\right)^{2}}=\sqrt{\frac{81}{400}}$$

Whakarūnātia.

$$a+\frac{21}{20}=\frac{9}{20} a+\frac{21}{20}=-\frac{9}{20}$$

Me tango \frac{21}{20} mai i ngā taha e rua o te whārite.

$$a=-\frac{3}{5} a=-\frac{3}{2}$$