Whakaoti i te 0=20x-5x^2

$$0=20x-5 { x }^{ 2 }$$

Whakaoti mō x

$$x=4$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$20x-5x^{2}=0$$

Tauwehea te x.

$$x\left(20-5x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 20-5x=0.

$$x=0 x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$20x-5x^{2}=0$$

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.

$$-5x^{2}+20x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 20 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 20^{2}.

$$x=\frac{-20±20}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$x=\frac{-20±20}{-10}$$

Nā, me whakaoti te whārite x=\frac{-20±20}{-10} ina he tāpiri te ±. Tāpiri -20 ki te 20.

$$x=\frac{0}{-10}$$

Whakawehe 0 ki te -10.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-20±20}{-10} ina he tango te ±. Tango 20 mai i -20.

$$x=-\frac{40}{-10}$$

Whakawehe -40 ki te -10.

$$x=4$$

Kua oti te whārite te whakatau.

$$x=0 x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$20x-5x^{2}=0$$

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.

$$-5x^{2}+20x=0$$

Whakawehea ngā taha e rua ki te -5.

$$\frac{-5x^{2}+20x}{-5}=\frac{0}{-5}$$

Mā te whakawehe ki te -5 ka wetekia te whakareanga ki te -5.

$$x^{2}+\frac{20}{-5}x=\frac{0}{-5}$$

Whakawehe 20 ki te -5.

$$x^{2}-4x=\frac{0}{-5}$$

Whakawehe 0 ki te -5.

$$x^{2}-4x=0$$

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.

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

Pūrua -2.

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

Tauwehea te x^{2}-4x+4. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

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

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

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

Whakarūnātia.

$$x-2=2 x-2=-2$$

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

$$x=4 x=0$$