Whakaoti i te 180*(x-2)-180(x-2)/x=180

$$180 \times (x-2)- \frac{ 180(x-2) }{ x } =180$$

Whakaoti mō x

$$x=\sqrt{2}+2\approx 3.414213562$$

$$x=2-\sqrt{2}\approx 0.585786438$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$180\left(x-2\right)x-180\left(x-2\right)=180x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 180 ki te x-2.

$$\left(180x-360\right)x-180\left(x-2\right)=180x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 180x-360 ki te x.

$$180x^{2}-360x-180\left(x-2\right)=180x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -180 ki te x-2.

$$180x^{2}-360x-180x+360=180x$$

Pahekotia te -360x me -180x, ka -540x.

$$180x^{2}-540x+360=180x$$

Tangohia te 180x mai i ngā taha e rua.

$$180x^{2}-540x+360-180x=0$$

Pahekotia te -540x me -180x, ka -720x.

$$180x^{2}-720x+360=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 180 mō a, -720 mō b, me 360 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-720\right)±\sqrt{\left(-720\right)^{2}-4\times 180\times 360}}{2\times 180}$$

Pūrua -720.

$$x=\frac{-\left(-720\right)±\sqrt{518400-4\times 180\times 360}}{2\times 180}$$

Whakareatia -4 ki te 180.

$$x=\frac{-\left(-720\right)±\sqrt{518400-720\times 360}}{2\times 180}$$

Whakareatia -720 ki te 360.

$$x=\frac{-\left(-720\right)±\sqrt{518400-259200}}{2\times 180}$$

Tāpiri 518400 ki te -259200.

$$x=\frac{-\left(-720\right)±\sqrt{259200}}{2\times 180}$$

Tuhia te pūtakerua o te 259200.

$$x=\frac{-\left(-720\right)±360\sqrt{2}}{2\times 180}$$

Ko te tauaro o -720 ko 720.

$$x=\frac{720±360\sqrt{2}}{2\times 180}$$

Whakareatia 2 ki te 180.

$$x=\frac{720±360\sqrt{2}}{360}$$

Nā, me whakaoti te whārite x=\frac{720±360\sqrt{2}}{360} ina he tāpiri te ±. Tāpiri 720 ki te 360\sqrt{2}.

$$x=\frac{360\sqrt{2}+720}{360}$$

Whakawehe 720+360\sqrt{2} ki te 360.

$$x=\sqrt{2}+2$$

Nā, me whakaoti te whārite x=\frac{720±360\sqrt{2}}{360} ina he tango te ±. Tango 360\sqrt{2} mai i 720.

$$x=\frac{720-360\sqrt{2}}{360}$$

Whakawehe 720-360\sqrt{2} ki te 360.

$$x=2-\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{2}+2 x=2-\sqrt{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$180\left(x-2\right)x-180\left(x-2\right)=180x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 180 ki te x-2.

$$\left(180x-360\right)x-180\left(x-2\right)=180x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 180x-360 ki te x.

$$180x^{2}-360x-180\left(x-2\right)=180x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -180 ki te x-2.

$$180x^{2}-360x-180x+360=180x$$

Pahekotia te -360x me -180x, ka -540x.

$$180x^{2}-540x+360=180x$$

Tangohia te 180x mai i ngā taha e rua.

$$180x^{2}-540x+360-180x=0$$

Pahekotia te -540x me -180x, ka -720x.

$$180x^{2}-720x+360=0$$

Tangohia te 360 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$180x^{2}-720x=-360$$

Whakawehea ngā taha e rua ki te 180.

$$\frac{180x^{2}-720x}{180}=-\frac{360}{180}$$

Mā te whakawehe ki te 180 ka wetekia te whakareanga ki te 180.

$$x^{2}+\left(-\frac{720}{180}\right)x=-\frac{360}{180}$$

Whakawehe -720 ki te 180.

$$x^{2}-4x=-\frac{360}{180}$$

Whakawehe -360 ki te 180.

$$x^{2}-4x=-2$$

Whakawehea te -4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2. Nā, tāpiria te pūrua o te -2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-4x+\left(-2\right)^{2}=-2+\left(-2\right)^{2}$$

Pūrua -2.

$$x^{2}-4x+4=-2+4$$

Tāpiri -2 ki te 4.

$$x^{2}-4x+4=2$$

Tauwehea x^{2}-4x+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}.

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

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{2}$$

Whakarūnātia.

$$x-2=\sqrt{2} x-2=-\sqrt{2}$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$x=\sqrt{2}+2 x=2-\sqrt{2}$$