Whakaoti i te 800*(1+x/10)*(1-x/10)=800-32

$$800 \times ( 1 + \frac { x } { 10 } ) \times ( 1 - \frac { x } { 10 } ) = 800 - 32$$

Whakaoti mō x

$$x=2$$

$$x=-2$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 10.

$$8000\left(1+\frac{x}{10}\right)\left(1-\frac{x}{10}\right)=8000-320$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8000 ki te 1+\frac{x}{10}.

$$\left(8000+8000\times \frac{x}{10}\right)\left(1-\frac{x}{10}\right)=8000-320$$

Whakakorea atu te tauwehe pūnoa nui rawa 10 i roto i te 8000 me te 10.

$$\left(8000+800x\right)\left(1-\frac{x}{10}\right)=8000-320$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 8000+800x ki ia tau o 1-\frac{x}{10}.

$$8000+8000\left(-\frac{x}{10}\right)+800x+800x\left(-\frac{x}{10}\right)=8000-320$$

Whakakorea atu te tauwehe pūnoa nui rawa 10 i roto i te 8000 me te 10.

$$8000-800x+800x+800x\left(-\frac{x}{10}\right)=8000-320$$

Pahekotia te -800x me 800x, ka 0.

$$8000+800x\left(-\frac{x}{10}\right)=8000-320$$

Whakakorea atu te tauwehe pūnoa nui rawa 10 i roto i te 800 me te 10.

$$8000-80xx=8000-320$$

Whakareatia te x ki te x, ka x^{2}.

$$8000-80x^{2}=8000-320$$

Tangohia te 320 i te 8000, ka 7680.

$$8000-80x^{2}=7680$$

Tangohia te 8000 mai i ngā taha e rua.

$$-80x^{2}=7680-8000$$

Tangohia te 8000 i te 7680, ka -320.

$$-80x^{2}=-320$$

Whakawehea ngā taha e rua ki te -80.

$$x^{2}=\frac{-320}{-80}$$

Whakawehea te -320 ki te -80, kia riro ko 4.

$$x^{2}=4$$

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

$$x=2 x=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 10.

$$8000\left(1+\frac{x}{10}\right)\left(1-\frac{x}{10}\right)=8000-320$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8000 ki te 1+\frac{x}{10}.

$$\left(8000+8000\times \frac{x}{10}\right)\left(1-\frac{x}{10}\right)=8000-320$$

Whakakorea atu te tauwehe pūnoa nui rawa 10 i roto i te 8000 me te 10.

$$\left(8000+800x\right)\left(1-\frac{x}{10}\right)=8000-320$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 8000+800x ki ia tau o 1-\frac{x}{10}.

$$8000+8000\left(-\frac{x}{10}\right)+800x+800x\left(-\frac{x}{10}\right)=8000-320$$

Whakakorea atu te tauwehe pūnoa nui rawa 10 i roto i te 8000 me te 10.

$$8000-800x+800x+800x\left(-\frac{x}{10}\right)=8000-320$$

Pahekotia te -800x me 800x, ka 0.

$$8000+800x\left(-\frac{x}{10}\right)=8000-320$$

Whakakorea atu te tauwehe pūnoa nui rawa 10 i roto i te 800 me te 10.

$$8000-80xx=8000-320$$

Whakareatia te x ki te x, ka x^{2}.

$$8000-80x^{2}=8000-320$$

Tangohia te 320 i te 8000, ka 7680.

$$8000-80x^{2}=7680$$

Tangohia te 7680 mai i ngā taha e rua.

$$8000-80x^{2}-7680=0$$

Tangohia te 7680 i te 8000, ka 320.

$$320-80x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-80x^{2}+320=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -80 mō a, 0 mō b, me 320 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-80\right)\times 320}}{2\left(-80\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-80\right)\times 320}}{2\left(-80\right)}$$

Whakareatia -4 ki te -80.

$$x=\frac{0±\sqrt{320\times 320}}{2\left(-80\right)}$$

Whakareatia 320 ki te 320.

$$x=\frac{0±\sqrt{102400}}{2\left(-80\right)}$$

Tuhia te pūtakerua o te 102400.

$$x=\frac{0±320}{2\left(-80\right)}$$

Whakareatia 2 ki te -80.

$$x=\frac{0±320}{-160}$$

Nā, me whakaoti te whārite x=\frac{0±320}{-160} ina he tāpiri te ±. Whakawehe 320 ki te -160.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{0±320}{-160} ina he tango te ±. Whakawehe -320 ki te -160.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=-2 x=2$$