Whakaoti i te a^2+8a+9=96

$$a ^ { 2 } + 8 a + 9 = 96$$

Whakaoti mō a (complex solution)

$$a=\sqrt{103}-4\approx 6.148891565$$

$$a=-\left(\sqrt{103}+4\right)\approx -14.148891565$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$a^{2}+8a+9=96$$

Me tango 96 mai i ngā taha e rua o te whārite.

$$a^{2}+8a+9-96=96-96$$

Mā te tango i te 96 i a ia ake anō ka toe ko te 0.

$$a^{2}+8a+9-96=0$$

Tango 96 mai i 9.

$$a^{2}+8a-87=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me -87 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-8±\sqrt{8^{2}-4\left(-87\right)}}{2}$$

Pūrua 8.

$$a=\frac{-8±\sqrt{64-4\left(-87\right)}}{2}$$

Whakareatia -4 ki te -87.

$$a=\frac{-8±\sqrt{64+348}}{2}$$

Tāpiri 64 ki te 348.

$$a=\frac{-8±\sqrt{412}}{2}$$

Tuhia te pūtakerua o te 412.

$$a=\frac{-8±2\sqrt{103}}{2}$$

Nā, me whakaoti te whārite a=\frac{-8±2\sqrt{103}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{103}.

$$a=\frac{2\sqrt{103}-8}{2}$$

Whakawehe -8+2\sqrt{103} ki te 2.

$$a=\sqrt{103}-4$$

Nā, me whakaoti te whārite a=\frac{-8±2\sqrt{103}}{2} ina he tango te ±. Tango 2\sqrt{103} mai i -8.

$$a=\frac{-2\sqrt{103}-8}{2}$$

Whakawehe -8-2\sqrt{103} ki te 2.

$$a=-\sqrt{103}-4$$

Kua oti te whārite te whakatau.

$$a=\sqrt{103}-4 a=-\sqrt{103}-4$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$a^{2}+8a+9=96$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$a^{2}+8a+9-9=96-9$$

Mā te tango i te 9 i a ia ake anō ka toe ko te 0.

$$a^{2}+8a=96-9$$

Tango 9 mai i 96.

$$a^{2}+8a=87$$

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.

$$a^{2}+8a+4^{2}=87+4^{2}$$

Pūrua 4.

$$a^{2}+8a+16=87+16$$

Tāpiri 87 ki te 16.

$$a^{2}+8a+16=103$$

Tauwehea a^{2}+8a+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}.

$$\left(a+4\right)^{2}=103$$

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

$$\sqrt{\left(a+4\right)^{2}}=\sqrt{103}$$

Whakarūnātia.

$$a+4=\sqrt{103} a+4=-\sqrt{103}$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$a=\sqrt{103}-4 a=-\sqrt{103}-4$$

Whakaoti mō a

$$a=\sqrt{103}-4\approx 6.148891565$$

$$a=-\sqrt{103}-4\approx -14.148891565$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$a^{2}+8a+9=96$$

Me tango 96 mai i ngā taha e rua o te whārite.

$$a^{2}+8a+9-96=96-96$$

Mā te tango i te 96 i a ia ake anō ka toe ko te 0.

$$a^{2}+8a+9-96=0$$

Tango 96 mai i 9.

$$a^{2}+8a-87=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me -87 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-8±\sqrt{8^{2}-4\left(-87\right)}}{2}$$

Pūrua 8.

$$a=\frac{-8±\sqrt{64-4\left(-87\right)}}{2}$$

Whakareatia -4 ki te -87.

$$a=\frac{-8±\sqrt{64+348}}{2}$$

Tāpiri 64 ki te 348.

$$a=\frac{-8±\sqrt{412}}{2}$$

Tuhia te pūtakerua o te 412.

$$a=\frac{-8±2\sqrt{103}}{2}$$

Nā, me whakaoti te whārite a=\frac{-8±2\sqrt{103}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{103}.

$$a=\frac{2\sqrt{103}-8}{2}$$

Whakawehe -8+2\sqrt{103} ki te 2.

$$a=\sqrt{103}-4$$

Nā, me whakaoti te whārite a=\frac{-8±2\sqrt{103}}{2} ina he tango te ±. Tango 2\sqrt{103} mai i -8.

$$a=\frac{-2\sqrt{103}-8}{2}$$

Whakawehe -8-2\sqrt{103} ki te 2.

$$a=-\sqrt{103}-4$$

Kua oti te whārite te whakatau.

$$a=\sqrt{103}-4 a=-\sqrt{103}-4$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$a^{2}+8a+9=96$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$a^{2}+8a+9-9=96-9$$

Mā te tango i te 9 i a ia ake anō ka toe ko te 0.

$$a^{2}+8a=96-9$$

Tango 9 mai i 96.

$$a^{2}+8a=87$$

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.

$$a^{2}+8a+4^{2}=87+4^{2}$$

Pūrua 4.

$$a^{2}+8a+16=87+16$$

Tāpiri 87 ki te 16.

$$a^{2}+8a+16=103$$

Tauwehea a^{2}+8a+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}.

$$\left(a+4\right)^{2}=103$$

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

$$\sqrt{\left(a+4\right)^{2}}=\sqrt{103}$$

Whakarūnātia.

$$a+4=\sqrt{103} a+4=-\sqrt{103}$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$a=\sqrt{103}-4 a=-\sqrt{103}-4$$