Whakaoti i te 5x^2=-9x-6

$$5 x ^ { 2 } = - 9 x - 6$$

Whakaoti mō x (complex solution)

$$x=\frac{-9+\sqrt{39}i}{10}\approx -0.9+0.6244998i$$

$$x=\frac{-\sqrt{39}i-9}{10}\approx -0.9-0.6244998i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 9x ki ngā taha e rua.

$$5x^{2}+9x=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$5x^{2}+9x+6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 9 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9±\sqrt{9^{2}-4\times 5\times 6}}{2\times 5}$$

Pūrua 9.

$$x=\frac{-9±\sqrt{81-4\times 5\times 6}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-9±\sqrt{81-20\times 6}}{2\times 5}$$

Whakareatia -20 ki te 6.

$$x=\frac{-9±\sqrt{81-120}}{2\times 5}$$

Tāpiri 81 ki te -120.

$$x=\frac{-9±\sqrt{-39}}{2\times 5}$$

Tuhia te pūtakerua o te -39.

$$x=\frac{-9±\sqrt{39}i}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-9±\sqrt{39}i}{10}$$

Nā, me whakaoti te whārite x=\frac{-9±\sqrt{39}i}{10} ina he tāpiri te ±. Tāpiri -9 ki te i\sqrt{39}.

$$x=\frac{-9+\sqrt{39}i}{10}$$

Nā, me whakaoti te whārite x=\frac{-9±\sqrt{39}i}{10} ina he tango te ±. Tango i\sqrt{39} mai i -9.

$$x=\frac{-\sqrt{39}i-9}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{-9+\sqrt{39}i}{10} x=\frac{-\sqrt{39}i-9}{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 9x ki ngā taha e rua.

$$5x^{2}+9x=-6$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}+9x}{5}=-\frac{6}{5}$$

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

$$x^{2}+\frac{9}{5}x=-\frac{6}{5}$$

Whakawehea te \frac{9}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{9}{10}. Nā, tāpiria te pūrua o te \frac{9}{10} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{9}{5}x+\left(\frac{9}{10}\right)^{2}=-\frac{6}{5}+\left(\frac{9}{10}\right)^{2}$$

Pūruatia \frac{9}{10} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{9}{5}x+\frac{81}{100}=-\frac{6}{5}+\frac{81}{100}$$

Tāpiri -\frac{6}{5} ki te \frac{81}{100} 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.

$$x^{2}+\frac{9}{5}x+\frac{81}{100}=-\frac{39}{100}$$

Tauwehea x^{2}+\frac{9}{5}x+\frac{81}{100}. 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}.

$$\left(x+\frac{9}{10}\right)^{2}=-\frac{39}{100}$$

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

$$\sqrt{\left(x+\frac{9}{10}\right)^{2}}=\sqrt{-\frac{39}{100}}$$

Whakarūnātia.

$$x+\frac{9}{10}=\frac{\sqrt{39}i}{10} x+\frac{9}{10}=-\frac{\sqrt{39}i}{10}$$

Me tango \frac{9}{10} mai i ngā taha e rua o te whārite.

$$x=\frac{-9+\sqrt{39}i}{10} x=\frac{-\sqrt{39}i-9}{10}$$