Whakaoti i te 3x^2-18x=0

$$3 { x }^{ 2 } -18x=0$$

Whakaoti mō x

$$x=6$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(3x-18\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 3x-18=0.

$$x=0 x=6$$

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.

$$3x^{2}-18x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -18 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2\times 3}$$

Tuhia te pūtakerua o te \left(-18\right)^{2}.

$$x=\frac{-\left(-18\right)±18}{2\times 3}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±18}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{18±18}{6}$$

Nā, me whakaoti te whārite x=\frac{18±18}{6} ina he tāpiri te ±. Tāpiri 18 ki te 18.

$$x=\frac{36}{6}$$

Whakawehe 36 ki te 6.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{18±18}{6} ina he tango te ±. Tango 18 mai i 18.

$$x=\frac{0}{6}$$

Whakawehe 0 ki te 6.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=6 x=0$$

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.

$$3x^{2}-18x=0$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-18x}{3}=\frac{0}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}+\left(-\frac{18}{3}\right)x=\frac{0}{3}$$

Whakawehe -18 ki te 3.

$$x^{2}-6x=\frac{0}{3}$$

Whakawehe 0 ki te 3.

$$x^{2}-6x=0$$

Whakawehea te -6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -3. Nā, tāpiria te pūrua o te -3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-6x+\left(-3\right)^{2}=\left(-3\right)^{2}$$

Pūrua -3.

$$x^{2}-6x+9=9$$

Tauwehea x^{2}-6x+9. 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}.

$$\left(x-3\right)^{2}=9$$

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

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$x-3=3 x-3=-3$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=6 x=0$$