Whakaoti i te 3x^2-24x=0

$$3 x ^ { 2 } - 24 x = 0$$

Whakaoti mō x

$$x=8$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(3x-24\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 3x-24=0.

$$x=0 x=8$$

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.

$$3x^{2}-24x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -24 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 3}$$

Tuhia te pūtakerua o te \left(-24\right)^{2}.

$$x=\frac{-\left(-24\right)±24}{2\times 3}$$

Ko te tauaro o -24 ko 24.

$$x=\frac{24±24}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{24±24}{6}$$

Nā, me whakaoti te whārite x=\frac{24±24}{6} ina he tāpiri te ±. Tāpiri 24 ki te 24.

$$x=\frac{48}{6}$$

Whakawehe 48 ki te 6.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{24±24}{6} ina he tango te ±. Tango 24 mai i 24.

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

Whakawehe 0 ki te 6.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=8 x=0$$

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.

$$3x^{2}-24x=0$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-24x}{3}=\frac{0}{3}$$

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

$$x^{2}+\left(-\frac{24}{3}\right)x=\frac{0}{3}$$

Whakawehe -24 ki te 3.

$$x^{2}-8x=\frac{0}{3}$$

Whakawehe 0 ki te 3.

$$x^{2}-8x=0$$

Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}$$

Pūrua -4.

$$x^{2}-8x+16=16$$

Tauwehea te x^{2}-8x+16. 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}.

$$\left(x-4\right)^{2}=16$$

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

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x-4=4 x-4=-4$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=8 x=0$$