Whakaoti i te 1000(1+x)(098+x)=1000(1+x)+108

$$1000(1+x)(098+x)=1000(1+x)+108$$

Whakaoti mō x

$$x = \frac{\sqrt{2770}}{50} \approx 1.052615789$$

$$x = -\frac{\sqrt{2770}}{50} \approx -1.052615789$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 0 ki te 98, ka 0.

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

Ko te tau i tāpiria he kore ka hua koia tonu.

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

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

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

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

$$1000x+1000x^{2}=1000\left(1+x\right)+108$$

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

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

Tāpirihia te 1000 ki te 108, ka 1108.

$$1000x+1000x^{2}=1108+1000x$$

Tangohia te 1000x mai i ngā taha e rua.

$$1000x+1000x^{2}-1000x=1108$$

Pahekotia te 1000x me -1000x, ka 0.

$$1000x^{2}=1108$$

Whakawehea ngā taha e rua ki te 1000.

$$x^{2}=\frac{1108}{1000}$$

Whakahekea te hautanga \frac{1108}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}=\frac{277}{250}$$

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

$$x=\frac{\sqrt{2770}}{50} x=-\frac{\sqrt{2770}}{50}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 98, ka 0.

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

Ko te tau i tāpiria he kore ka hua koia tonu.

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

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

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

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

$$1000x+1000x^{2}=1000\left(1+x\right)+108$$

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

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

Tāpirihia te 1000 ki te 108, ka 1108.

$$1000x+1000x^{2}=1108+1000x$$

Tangohia te 1108 mai i ngā taha e rua.

$$1000x+1000x^{2}-1108=1000x$$

Tangohia te 1000x mai i ngā taha e rua.

$$1000x+1000x^{2}-1108-1000x=0$$

Pahekotia te 1000x me -1000x, ka 0.

$$1000x^{2}-1108=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1000 mō a, 0 mō b, me -1108 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1000\left(-1108\right)}}{2\times 1000}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 1000\left(-1108\right)}}{2\times 1000}$$

Whakareatia -4 ki te 1000.

$$x=\frac{0±\sqrt{-4000\left(-1108\right)}}{2\times 1000}$$

Whakareatia -4000 ki te -1108.

$$x=\frac{0±\sqrt{4432000}}{2\times 1000}$$

Tuhia te pūtakerua o te 4432000.

$$x=\frac{0±40\sqrt{2770}}{2\times 1000}$$

Whakareatia 2 ki te 1000.

$$x=\frac{0±40\sqrt{2770}}{2000}$$

Nā, me whakaoti te whārite x=\frac{0±40\sqrt{2770}}{2000} ina he tāpiri te ±.

$$x=\frac{\sqrt{2770}}{50}$$

Nā, me whakaoti te whārite x=\frac{0±40\sqrt{2770}}{2000} ina he tango te ±.

$$x=-\frac{\sqrt{2770}}{50}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{2770}}{50} x=-\frac{\sqrt{2770}}{50}$$