Whakaoti i te 4x^2-12x=0

$$4 x ^ { 2 } - 12 x = 0$$

Whakaoti mō x

$$x=3$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(4x-12\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 4x-12=0.

$$x=0 x=3$$

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.

$$4x^{2}-12x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -12 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\times 4}$$

Tuhia te pūtakerua o te \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2\times 4}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±12}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{12±12}{8}$$

Nā, me whakaoti te whārite x=\frac{12±12}{8} ina he tāpiri te ±. Tāpiri 12 ki te 12.

$$x=\frac{24}{8}$$

Whakawehe 24 ki te 8.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{12±12}{8} ina he tango te ±. Tango 12 mai i 12.

$$x=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=3 x=0$$

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.

$$4x^{2}-12x=0$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}-12x}{4}=\frac{0}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}+\left(-\frac{12}{4}\right)x=\frac{0}{4}$$

Whakawehe -12 ki te 4.

$$x^{2}-3x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

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

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

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

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=\frac{9}{4}$$

Tauwehea x^{2}-3x+\frac{9}{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}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$x-\frac{3}{2}=\frac{3}{2} x-\frac{3}{2}=-\frac{3}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=3 x=0$$