Whakaoti i te a^2+12a/5=3

$$a ^ { 2 } + \frac { 12 a } { 5 } = 3$$

Whakaoti mō a

$$a=\frac{\sqrt{111}-6}{5}\approx 0.907130751$$

$$a=\frac{-\sqrt{111}-6}{5}\approx -3.307130751$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 5.

$$5a^{2}+12a=15$$

Tangohia te 15 mai i ngā taha e rua.

$$5a^{2}+12a-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 12 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-12±\sqrt{12^{2}-4\times 5\left(-15\right)}}{2\times 5}$$

Pūrua 12.

$$a=\frac{-12±\sqrt{144-4\times 5\left(-15\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$a=\frac{-12±\sqrt{144-20\left(-15\right)}}{2\times 5}$$

Whakareatia -20 ki te -15.

$$a=\frac{-12±\sqrt{144+300}}{2\times 5}$$

Tāpiri 144 ki te 300.

$$a=\frac{-12±\sqrt{444}}{2\times 5}$$

Tuhia te pūtakerua o te 444.

$$a=\frac{-12±2\sqrt{111}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$a=\frac{-12±2\sqrt{111}}{10}$$

Nā, me whakaoti te whārite a=\frac{-12±2\sqrt{111}}{10} ina he tāpiri te ±. Tāpiri -12 ki te 2\sqrt{111}.

$$a=\frac{2\sqrt{111}-12}{10}$$

Whakawehe -12+2\sqrt{111} ki te 10.

$$a=\frac{\sqrt{111}-6}{5}$$

Nā, me whakaoti te whārite a=\frac{-12±2\sqrt{111}}{10} ina he tango te ±. Tango 2\sqrt{111} mai i -12.

$$a=\frac{-2\sqrt{111}-12}{10}$$

Whakawehe -12-2\sqrt{111} ki te 10.

$$a=\frac{-\sqrt{111}-6}{5}$$

Kua oti te whārite te whakatau.

$$a=\frac{\sqrt{111}-6}{5} a=\frac{-\sqrt{111}-6}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 5.

$$5a^{2}+12a=15$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5a^{2}+12a}{5}=\frac{15}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$a^{2}+\frac{12}{5}a=\frac{15}{5}$$

Whakawehe 15 ki te 5.

$$a^{2}+\frac{12}{5}a=3$$

Whakawehea te \frac{12}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{6}{5}. Nā, tāpiria te pūrua o te \frac{6}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}+\frac{12}{5}a+\left(\frac{6}{5}\right)^{2}=3+\left(\frac{6}{5}\right)^{2}$$

Pūruatia \frac{6}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}+\frac{12}{5}a+\frac{36}{25}=3+\frac{36}{25}$$

Tāpiri 3 ki te \frac{36}{25}.

$$a^{2}+\frac{12}{5}a+\frac{36}{25}=\frac{111}{25}$$

Tauwehea a^{2}+\frac{12}{5}a+\frac{36}{25}. 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}.

$$\left(a+\frac{6}{5}\right)^{2}=\frac{111}{25}$$

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

$$\sqrt{\left(a+\frac{6}{5}\right)^{2}}=\sqrt{\frac{111}{25}}$$

Whakarūnātia.

$$a+\frac{6}{5}=\frac{\sqrt{111}}{5} a+\frac{6}{5}=-\frac{\sqrt{111}}{5}$$

Me tango \frac{6}{5} mai i ngā taha e rua o te whārite.

$$a=\frac{\sqrt{111}-6}{5} a=\frac{-\sqrt{111}-6}{5}$$