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

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

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}.

$$x=\frac{-24±\sqrt{24^{2}}}{2\times 3}$$

Tuhia te pūtakerua o te 24^{2}.

$$x=\frac{-24±24}{2\times 3}$$

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.

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

Whakawehe 0 ki te 6.

$$x=0$$

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

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

Whakawehe -48 ki te 6.

$$x=-8$$

Kua oti te whārite te whakatau.

$$x=0 x=-8$$

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.

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

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.

$$x^{2}+8x+4^{2}=4^{2}$$

Pūrua 4.

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

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

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

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 tango 4 mai i ngā taha e rua o te whārite.

$$x=0 x=-8$$