Whakaoti i te 2a^2+8a+6=5/2

$$2 a ^ { 2 } + 8 a + 6 = \frac { 5 } { 2 }$$

Whakaoti mō a

$$a = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

$$a=-\frac{1}{2}=-0.5$$

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.

$$2a^{2}+8a+6=\frac{5}{2}$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$2a^{2}+8a+6-\frac{5}{2}=\frac{5}{2}-\frac{5}{2}$$

Mā te tango i te \frac{5}{2} i a ia ake anō ka toe ko te 0.

$$2a^{2}+8a+6-\frac{5}{2}=0$$

Tango \frac{5}{2} mai i 6.

$$2a^{2}+8a+\frac{7}{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 8 mō b, me \frac{7}{2} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-8±\sqrt{8^{2}-4\times 2\times \frac{7}{2}}}{2\times 2}$$

Pūrua 8.

$$a=\frac{-8±\sqrt{64-4\times 2\times \frac{7}{2}}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$a=\frac{-8±\sqrt{64-8\times \frac{7}{2}}}{2\times 2}$$

Whakareatia -8 ki te \frac{7}{2}.

$$a=\frac{-8±\sqrt{64-28}}{2\times 2}$$

Tāpiri 64 ki te -28.

$$a=\frac{-8±\sqrt{36}}{2\times 2}$$

Tuhia te pūtakerua o te 36.

$$a=\frac{-8±6}{2\times 2}$$

Whakareatia 2 ki te 2.

$$a=\frac{-8±6}{4}$$

Nā, me whakaoti te whārite a=\frac{-8±6}{4} ina he tāpiri te ±. Tāpiri -8 ki te 6.

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

Whakahekea te hautanga \frac{-2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Nā, me whakaoti te whārite a=\frac{-8±6}{4} ina he tango te ±. Tango 6 mai i -8.

$$a=-\frac{14}{4}$$

Whakahekea te hautanga \frac{-14}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$a=-\frac{7}{2}$$

Kua oti te whārite te whakatau.

$$a=-\frac{1}{2} a=-\frac{7}{2}$$

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.

$$2a^{2}+8a+6=\frac{5}{2}$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$2a^{2}+8a+6-6=\frac{5}{2}-6$$

Mā te tango i te 6 i a ia ake anō ka toe ko te 0.

$$2a^{2}+8a=\frac{5}{2}-6$$

Tango 6 mai i \frac{5}{2}.

$$2a^{2}+8a=-\frac{7}{2}$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2a^{2}+8a}{2}=-\frac{\frac{7}{2}}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$a^{2}+\frac{8}{2}a=-\frac{\frac{7}{2}}{2}$$

Whakawehe 8 ki te 2.

$$a^{2}+4a=-\frac{\frac{7}{2}}{2}$$

Whakawehe -\frac{7}{2} ki te 2.

$$a^{2}+4a=-\frac{7}{4}$$

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.

$$a^{2}+4a+2^{2}=-\frac{7}{4}+2^{2}$$

Pūrua 2.

$$a^{2}+4a+4=-\frac{7}{4}+4$$

Tāpiri -\frac{7}{4} ki te 4.

$$a^{2}+4a+4=\frac{9}{4}$$

Tauwehea a^{2}+4a+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}.

$$\left(a+2\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(a+2\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

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

Me tango 2 mai i ngā taha e rua o te whārite.

$$a=-\frac{1}{2} a=-\frac{7}{2}$$