Whakaoti i te 1000x(1+x-002)=108

$$1000x(1+x-002)=108$$

Whakaoti mō x

$$x=\frac{\sqrt{895}}{50}-\frac{1}{2}\approx 0.098331012$$

$$x=-\frac{\sqrt{895}}{50}-\frac{1}{2}\approx -1.098331012$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 0, ka 0.

$$1000x\left(1+x-0\times 2\right)=108$$

Whakareatia te 0 ki te 2, ka 0.

$$1000x\left(1+x-0\right)=108$$

Tangohia te 108 mai i ngā taha e rua.

$$1000x\left(1+x-0\right)-108=0$$

Whakaraupapatia anō ngā kīanga tau.

$$1000x\left(x+1\right)-108=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1000x ki te x+1.

$$1000x^{2}+1000x-108=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1000 mō a, 1000 mō b, me -108 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1000±\sqrt{1000^{2}-4\times 1000\left(-108\right)}}{2\times 1000}$$

Pūrua 1000.

$$x=\frac{-1000±\sqrt{1000000-4\times 1000\left(-108\right)}}{2\times 1000}$$

Whakareatia -4 ki te 1000.

$$x=\frac{-1000±\sqrt{1000000-4000\left(-108\right)}}{2\times 1000}$$

Whakareatia -4000 ki te -108.

$$x=\frac{-1000±\sqrt{1000000+432000}}{2\times 1000}$$

Tāpiri 1000000 ki te 432000.

$$x=\frac{-1000±\sqrt{1432000}}{2\times 1000}$$

Tuhia te pūtakerua o te 1432000.

$$x=\frac{-1000±40\sqrt{895}}{2\times 1000}$$

Whakareatia 2 ki te 1000.

$$x=\frac{-1000±40\sqrt{895}}{2000}$$

Nā, me whakaoti te whārite x=\frac{-1000±40\sqrt{895}}{2000} ina he tāpiri te ±. Tāpiri -1000 ki te 40\sqrt{895}.

$$x=\frac{40\sqrt{895}-1000}{2000}$$

Whakawehe -1000+40\sqrt{895} ki te 2000.

$$x=\frac{\sqrt{895}}{50}-\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{-1000±40\sqrt{895}}{2000} ina he tango te ±. Tango 40\sqrt{895} mai i -1000.

$$x=\frac{-40\sqrt{895}-1000}{2000}$$

Whakawehe -1000-40\sqrt{895} ki te 2000.

$$x=-\frac{\sqrt{895}}{50}-\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{895}}{50}-\frac{1}{2} x=-\frac{\sqrt{895}}{50}-\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 0, ka 0.

$$1000x\left(1+x-0\times 2\right)=108$$

Whakareatia te 0 ki te 2, ka 0.

$$1000x\left(1+x-0\right)=108$$

Whakaraupapatia anō ngā kīanga tau.

$$1000x\left(x+1\right)=108$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1000x ki te x+1.

$$1000x^{2}+1000x=108$$

Whakawehea ngā taha e rua ki te 1000.

$$\frac{1000x^{2}+1000x}{1000}=\frac{108}{1000}$$

Mā te whakawehe ki te 1000 ka wetekia te whakareanga ki te 1000.

$$x^{2}+\frac{1000}{1000}x=\frac{108}{1000}$$

Whakawehe 1000 ki te 1000.

$$x^{2}+x=\frac{108}{1000}$$

Whakahekea te hautanga \frac{108}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}+x=\frac{27}{250}$$

Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\frac{27}{250}+\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+x+\frac{1}{4}=\frac{27}{250}+\frac{1}{4}$$

Tāpiri \frac{27}{250} ki te \frac{1}{4} 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.

$$x^{2}+x+\frac{1}{4}=\frac{179}{500}$$

Tauwehea x^{2}+x+\frac{1}{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}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{179}{500}$$

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

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{179}{500}}$$

Whakarūnātia.

$$x+\frac{1}{2}=\frac{\sqrt{895}}{50} x+\frac{1}{2}=-\frac{\sqrt{895}}{50}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{895}}{50}-\frac{1}{2} x=-\frac{\sqrt{895}}{50}-\frac{1}{2}$$