Whakaoti i te 1/50x(35000-x)=0

$$\frac { 1 } { 50 } x ( 35000 - x ) = 0$$

Whakaoti mō x

$$x=35000$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{50}x ki te 35000-x.

$$\frac{1}{50}x\times 35000+\frac{1}{50}x\left(-1\right)x=0$$

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

$$\frac{1}{50}x\times 35000+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakareatia te \frac{1}{50} ki te 35000, ka \frac{35000}{50}.

$$\frac{35000}{50}x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakawehea te 35000 ki te 50, kia riro ko 700.

$$700x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakareatia te \frac{1}{50} ki te -1, ka -\frac{1}{50}.

$$700x-\frac{1}{50}x^{2}=0$$

Tauwehea te x.

$$x\left(700-\frac{1}{50}x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 700-\frac{x}{50}=0.

$$x=0 x=35000$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{50}x ki te 35000-x.

$$\frac{1}{50}x\times 35000+\frac{1}{50}x\left(-1\right)x=0$$

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

$$\frac{1}{50}x\times 35000+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakareatia te \frac{1}{50} ki te 35000, ka \frac{35000}{50}.

$$\frac{35000}{50}x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakawehea te 35000 ki te 50, kia riro ko 700.

$$700x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakareatia te \frac{1}{50} ki te -1, ka -\frac{1}{50}.

$$700x-\frac{1}{50}x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-\frac{1}{50}x^{2}+700x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -\frac{1}{50} mō a, 700 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-700±\sqrt{700^{2}}}{2\left(-\frac{1}{50}\right)}$$

Tuhia te pūtakerua o te 700^{2}.

$$x=\frac{-700±700}{2\left(-\frac{1}{50}\right)}$$

Whakareatia 2 ki te -\frac{1}{50}.

$$x=\frac{-700±700}{-\frac{1}{25}}$$

Nā, me whakaoti te whārite x=\frac{-700±700}{-\frac{1}{25}} ina he tāpiri te ±. Tāpiri -700 ki te 700.

$$x=\frac{0}{-\frac{1}{25}}$$

Whakawehe 0 ki te -\frac{1}{25} mā te whakarea 0 ki te tau huripoki o -\frac{1}{25}.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-700±700}{-\frac{1}{25}} ina he tango te ±. Tango 700 mai i -700.

$$x=-\frac{1400}{-\frac{1}{25}}$$

Whakawehe -1400 ki te -\frac{1}{25} mā te whakarea -1400 ki te tau huripoki o -\frac{1}{25}.

$$x=35000$$

Kua oti te whārite te whakatau.

$$x=0 x=35000$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{50}x ki te 35000-x.

$$\frac{1}{50}x\times 35000+\frac{1}{50}x\left(-1\right)x=0$$

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

$$\frac{1}{50}x\times 35000+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakareatia te \frac{1}{50} ki te 35000, ka \frac{35000}{50}.

$$\frac{35000}{50}x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakawehea te 35000 ki te 50, kia riro ko 700.

$$700x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Whakareatia te \frac{1}{50} ki te -1, ka -\frac{1}{50}.

$$700x-\frac{1}{50}x^{2}=0$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-\frac{1}{50}x^{2}+700x=0$$

Me whakarea ngā taha e rua ki te -50.

$$\frac{-\frac{1}{50}x^{2}+700x}{-\frac{1}{50}}=\frac{0}{-\frac{1}{50}}$$

Mā te whakawehe ki te -\frac{1}{50} ka wetekia te whakareanga ki te -\frac{1}{50}.

$$x^{2}+\frac{700}{-\frac{1}{50}}x=\frac{0}{-\frac{1}{50}}$$

Whakawehe 700 ki te -\frac{1}{50} mā te whakarea 700 ki te tau huripoki o -\frac{1}{50}.

$$x^{2}-35000x=\frac{0}{-\frac{1}{50}}$$

Whakawehe 0 ki te -\frac{1}{50} mā te whakarea 0 ki te tau huripoki o -\frac{1}{50}.

$$x^{2}-35000x=0$$

Whakawehea te -35000, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -17500. Nā, tāpiria te pūrua o te -17500 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-35000x+\left(-17500\right)^{2}=\left(-17500\right)^{2}$$

Pūrua -17500.

$$x^{2}-35000x+306250000=306250000$$

Tauwehea x^{2}-35000x+306250000. 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}.

$$\left(x-17500\right)^{2}=306250000$$

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

$$\sqrt{\left(x-17500\right)^{2}}=\sqrt{306250000}$$

Whakarūnātia.

$$x-17500=17500 x-17500=-17500$$

Me tāpiri 17500 ki ngā taha e rua o te whārite.

$$x=35000 x=0$$