Whakaoti i te -500000x^2+45x-9*10^-6=0

$$-500000 { x }^{ 2 } +45x-9 \times { 10 }^{ -6 } = 0$$

Whakaoti mō x

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}\approx 0.0000898$$

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}\approx 0.0000002$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 10 mā te pū o -6, kia riro ko \frac{1}{1000000}.

$$-500000x^{2}+45x-9\times \frac{1}{1000000}=0$$

Whakareatia te 9 ki te \frac{1}{1000000}, ka \frac{9}{1000000}.

$$-500000x^{2}+45x-\frac{9}{1000000}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -500000 mō a, 45 mō b, me -\frac{9}{1000000} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-45±\sqrt{45^{2}-4\left(-500000\right)\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Pūrua 45.

$$x=\frac{-45±\sqrt{2025-4\left(-500000\right)\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Whakareatia -4 ki te -500000.

$$x=\frac{-45±\sqrt{2025+2000000\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Whakareatia 2000000 ki te -\frac{9}{1000000}.

$$x=\frac{-45±\sqrt{2025-18}}{2\left(-500000\right)}$$

Tāpiri 2025 ki te -18.

$$x=\frac{-45±\sqrt{2007}}{2\left(-500000\right)}$$

Tuhia te pūtakerua o te 2007.

$$x=\frac{-45±3\sqrt{223}}{2\left(-500000\right)}$$

Whakareatia 2 ki te -500000.

$$x=\frac{-45±3\sqrt{223}}{-1000000}$$

Nā, me whakaoti te whārite x=\frac{-45±3\sqrt{223}}{-1000000} ina he tāpiri te ±. Tāpiri -45 ki te 3\sqrt{223}.

$$x=\frac{3\sqrt{223}-45}{-1000000}$$

Whakawehe -45+3\sqrt{223} ki te -1000000.

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Nā, me whakaoti te whārite x=\frac{-45±3\sqrt{223}}{-1000000} ina he tango te ±. Tango 3\sqrt{223} mai i -45.

$$x=\frac{-3\sqrt{223}-45}{-1000000}$$

Whakawehe -45-3\sqrt{223} ki te -1000000.

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Kua oti te whārite te whakatau.

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000} x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 10 mā te pū o -6, kia riro ko \frac{1}{1000000}.

$$-500000x^{2}+45x-9\times \frac{1}{1000000}=0$$

Whakareatia te 9 ki te \frac{1}{1000000}, ka \frac{9}{1000000}.

$$-500000x^{2}+45x-\frac{9}{1000000}=0$$

Me tāpiri te \frac{9}{1000000} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-500000x^{2}+45x=\frac{9}{1000000}$$

Whakawehea ngā taha e rua ki te -500000.

$$\frac{-500000x^{2}+45x}{-500000}=\frac{\frac{9}{1000000}}{-500000}$$

Mā te whakawehe ki te -500000 ka wetekia te whakareanga ki te -500000.

$$x^{2}+\frac{45}{-500000}x=\frac{\frac{9}{1000000}}{-500000}$$

Whakahekea te hautanga \frac{45}{-500000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x^{2}-\frac{9}{100000}x=\frac{\frac{9}{1000000}}{-500000}$$

Whakawehe \frac{9}{1000000} ki te -500000.

$$x^{2}-\frac{9}{100000}x=-\frac{9}{500000000000}$$

Whakawehea te -\frac{9}{100000}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{200000}. Nā, tāpiria te pūrua o te -\frac{9}{200000} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{9}{100000}x+\left(-\frac{9}{200000}\right)^{2}=-\frac{9}{500000000000}+\left(-\frac{9}{200000}\right)^{2}$$

Pūruatia -\frac{9}{200000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}=-\frac{9}{500000000000}+\frac{81}{40000000000}$$

Tāpiri -\frac{9}{500000000000} ki te \frac{81}{40000000000} 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.

$$x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}=\frac{2007}{1000000000000}$$

Tauwehea x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}. 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}.

$$\left(x-\frac{9}{200000}\right)^{2}=\frac{2007}{1000000000000}$$

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

$$\sqrt{\left(x-\frac{9}{200000}\right)^{2}}=\sqrt{\frac{2007}{1000000000000}}$$

Whakarūnātia.

$$x-\frac{9}{200000}=\frac{3\sqrt{223}}{1000000} x-\frac{9}{200000}=-\frac{3\sqrt{223}}{1000000}$$

Me tāpiri \frac{9}{200000} ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000} x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$