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

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

Whakaoti mō x

$$x=4$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

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

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

$$x=0 x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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}.

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

Tuhia te pūtakerua o te \left(-20\right)^{2}.

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

Ko te tauaro o -20 ko 20.

$$x=\frac{20±20}{2\times 5}$$

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.

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

Whakawehe 40 ki te 10.

$$x=4$$

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

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

Whakawehe 0 ki te 10.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=4 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$x^{2}+\left(-\frac{20}{5}\right)x=\frac{0}{5}$$

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 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}.

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

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.

$$x=4 x=0$$