Whakaoti i te xleft(x+1right)/2=1923(x-1)

$$\frac{ x \left( x+1 \right) }{ 2 } = 1923(x-1)$$

Whakaoti mō x

$$x = \frac{\sqrt{14768641} + 3845}{2} \approx 3843.999479573$$

$$x = \frac{3845 - \sqrt{14768641}}{2} \approx 1.000520427$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$x\left(x+1\right)=3846\left(x-1\right)$$

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

$$x^{2}+x=3846\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3846 ki te x-1.

$$x^{2}+x=3846x-3846$$

Tangohia te 3846x mai i ngā taha e rua.

$$x^{2}+x-3846x=-3846$$

Pahekotia te x me -3846x, ka -3845x.

$$x^{2}-3845x=-3846$$

Me tāpiri te 3846 ki ngā taha e rua.

$$x^{2}-3845x+3846=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3845 mō b, me 3846 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3845\right)±\sqrt{\left(-3845\right)^{2}-4\times 3846}}{2}$$

Pūrua -3845.

$$x=\frac{-\left(-3845\right)±\sqrt{14784025-4\times 3846}}{2}$$

Whakareatia -4 ki te 3846.

$$x=\frac{-\left(-3845\right)±\sqrt{14784025-15384}}{2}$$

Tāpiri 14784025 ki te -15384.

$$x=\frac{-\left(-3845\right)±\sqrt{14768641}}{2}$$

Ko te tauaro o -3845 ko 3845.

$$x=\frac{3845±\sqrt{14768641}}{2}$$

Nā, me whakaoti te whārite x=\frac{3845±\sqrt{14768641}}{2} ina he tāpiri te ±. Tāpiri 3845 ki te \sqrt{14768641}.

$$x=\frac{\sqrt{14768641}+3845}{2}$$

Nā, me whakaoti te whārite x=\frac{3845±\sqrt{14768641}}{2} ina he tango te ±. Tango \sqrt{14768641} mai i 3845.

$$x=\frac{3845-\sqrt{14768641}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{14768641}+3845}{2} x=\frac{3845-\sqrt{14768641}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$x\left(x+1\right)=3846\left(x-1\right)$$

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

$$x^{2}+x=3846\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3846 ki te x-1.

$$x^{2}+x=3846x-3846$$

Tangohia te 3846x mai i ngā taha e rua.

$$x^{2}+x-3846x=-3846$$

Pahekotia te x me -3846x, ka -3845x.

$$x^{2}-3845x=-3846$$

Whakawehea te -3845, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3845}{2}. Nā, tāpiria te pūrua o te -\frac{3845}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-3845x+\left(-\frac{3845}{2}\right)^{2}=-3846+\left(-\frac{3845}{2}\right)^{2}$$

Pūruatia -\frac{3845}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3845x+\frac{14784025}{4}=-3846+\frac{14784025}{4}$$

Tāpiri -3846 ki te \frac{14784025}{4}.

$$x^{2}-3845x+\frac{14784025}{4}=\frac{14768641}{4}$$

Tauwehea x^{2}-3845x+\frac{14784025}{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}.

$$\left(x-\frac{3845}{2}\right)^{2}=\frac{14768641}{4}$$

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

$$\sqrt{\left(x-\frac{3845}{2}\right)^{2}}=\sqrt{\frac{14768641}{4}}$$

Whakarūnātia.

$$x-\frac{3845}{2}=\frac{\sqrt{14768641}}{2} x-\frac{3845}{2}=-\frac{\sqrt{14768641}}{2}$$

Me tāpiri \frac{3845}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{14768641}+3845}{2} x=\frac{3845-\sqrt{14768641}}{2}$$