Whakaoti i te 14-9a^2=-16-4a^2

$$14 - 9 a ^ { 2 } = - 16 - 4 a ^ { 2 }$$

Whakaoti mō a

$$a=\sqrt{6}\approx 2.449489743$$

$$a=-\sqrt{6}\approx -2.449489743$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 4a^{2} ki ngā taha e rua.

$$14-9a^{2}+4a^{2}=-16$$

Pahekotia te -9a^{2} me 4a^{2}, ka -5a^{2}.

$$14-5a^{2}=-16$$

Tangohia te 14 mai i ngā taha e rua.

$$-5a^{2}=-16-14$$

Tangohia te 14 i te -16, ka -30.

$$-5a^{2}=-30$$

Whakawehea ngā taha e rua ki te -5.

$$a^{2}=\frac{-30}{-5}$$

Whakawehea te -30 ki te -5, kia riro ko 6.

$$a^{2}=6$$

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

$$a=\sqrt{6} a=-\sqrt{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te -16 mai i ngā taha e rua.

$$14-9a^{2}-\left(-16\right)=-4a^{2}$$

Ko te tauaro o -16 ko 16.

$$14-9a^{2}+16=-4a^{2}$$

Me tāpiri te 4a^{2} ki ngā taha e rua.

$$14-9a^{2}+16+4a^{2}=0$$

Tāpirihia te 14 ki te 16, ka 30.

$$30-9a^{2}+4a^{2}=0$$

Pahekotia te -9a^{2} me 4a^{2}, ka -5a^{2}.

$$30-5a^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-5a^{2}+30=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 0 mō b, me 30 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 30}}{2\left(-5\right)}$$

Pūrua 0.

$$a=\frac{0±\sqrt{-4\left(-5\right)\times 30}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$a=\frac{0±\sqrt{20\times 30}}{2\left(-5\right)}$$

Whakareatia 20 ki te 30.

$$a=\frac{0±\sqrt{600}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 600.

$$a=\frac{0±10\sqrt{6}}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$a=\frac{0±10\sqrt{6}}{-10}$$

Nā, me whakaoti te whārite a=\frac{0±10\sqrt{6}}{-10} ina he tāpiri te ±.

$$a=-\sqrt{6}$$

Nā, me whakaoti te whārite a=\frac{0±10\sqrt{6}}{-10} ina he tango te ±.

$$a=\sqrt{6}$$

Kua oti te whārite te whakatau.

$$a=-\sqrt{6} a=\sqrt{6}$$