Whakaoti i te 12x^2=48x

$$12 x ^ { 2 } = 48 x$$

Whakaoti mō x

$$x=4$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 48x mai i ngā taha e rua.

$$12x^{2}-48x=0$$

Tauwehea te x.

$$x\left(12x-48\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 12x-48=0.

$$x=0 x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 48x mai i ngā taha e rua.

$$12x^{2}-48x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, -48 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-48\right)±\sqrt{\left(-48\right)^{2}}}{2\times 12}$$

Tuhia te pūtakerua o te \left(-48\right)^{2}.

$$x=\frac{-\left(-48\right)±48}{2\times 12}$$

Ko te tauaro o -48 ko 48.

$$x=\frac{48±48}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{48±48}{24}$$

Nā, me whakaoti te whārite x=\frac{48±48}{24} ina he tāpiri te ±. Tāpiri 48 ki te 48.

$$x=\frac{96}{24}$$

Whakawehe 96 ki te 24.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{48±48}{24} ina he tango te ±. Tango 48 mai i 48.

$$x=\frac{0}{24}$$

Whakawehe 0 ki te 24.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=4 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 48x mai i ngā taha e rua.

$$12x^{2}-48x=0$$

Whakawehea ngā taha e rua ki te 12.

$$\frac{12x^{2}-48x}{12}=\frac{0}{12}$$

Mā te whakawehe ki te 12 ka wetekia te whakareanga ki te 12.

$$x^{2}+\left(-\frac{48}{12}\right)x=\frac{0}{12}$$

Whakawehe -48 ki te 12.

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

Whakawehe 0 ki te 12.

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

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.

$$x=4 x=0$$