Whakaoti i te 3xleft(x-4right)=4x(x-4)

$$3x \left( x-4 \right) = 4x(x-4)$$

Whakaoti mō x

$$x=4$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-4.

$$3x^{2}-12x=4x\left(x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x-4.

$$3x^{2}-12x=4x^{2}-16x$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$3x^{2}-12x-4x^{2}=-16x$$

Pahekotia te 3x^{2} me -4x^{2}, ka -x^{2}.

$$-x^{2}-12x=-16x$$

Me tāpiri te 16x ki ngā taha e rua.

$$-x^{2}-12x+16x=0$$

Pahekotia te -12x me 16x, ka 4x.

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

Tauwehea te x.

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

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

$$x=0 x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-4.

$$3x^{2}-12x=4x\left(x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x-4.

$$3x^{2}-12x=4x^{2}-16x$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$3x^{2}-12x-4x^{2}=-16x$$

Pahekotia te 3x^{2} me -4x^{2}, ka -x^{2}.

$$-x^{2}-12x=-16x$$

Me tāpiri te 16x ki ngā taha e rua.

$$-x^{2}-12x+16x=0$$

Pahekotia te -12x me 16x, ka 4x.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 4 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 4^{2}.

$$x=\frac{-4±4}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-4±4}{-2}$$

Nā, me whakaoti te whārite x=\frac{-4±4}{-2} ina he tāpiri te ±. Tāpiri -4 ki te 4.

$$x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-4±4}{-2} ina he tango te ±. Tango 4 mai i -4.

$$x=-\frac{8}{-2}$$

Whakawehe -8 ki te -2.

$$x=4$$

Kua oti te whārite te whakatau.

$$x=0 x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-4.

$$3x^{2}-12x=4x\left(x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x-4.

$$3x^{2}-12x=4x^{2}-16x$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$3x^{2}-12x-4x^{2}=-16x$$

Pahekotia te 3x^{2} me -4x^{2}, ka -x^{2}.

$$-x^{2}-12x=-16x$$

Me tāpiri te 16x ki ngā taha e rua.

$$-x^{2}-12x+16x=0$$

Pahekotia te -12x me 16x, ka 4x.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+4x}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{4}{-1}x=\frac{0}{-1}$$

Whakawehe 4 ki te -1.

$$x^{2}-4x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

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

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.

$$x=4 x=0$$