Whakaoti i te (x-6)(4x)=(x)(8)

$$(x-6)(4x)=(x)(8)$$

Whakaoti mō x

$$x=8$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te x-6 ki te 4.

$$\left(4x-24\right)x=x\times 8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-24 ki te x.

$$4x^{2}-24x=x\times 8$$

Tangohia te x\times 8 mai i ngā taha e rua.

$$4x^{2}-24x-x\times 8=0$$

Pahekotia te -24x me -x\times 8, ka -32x.

$$4x^{2}-32x=0$$

Tauwehea te x.

$$x\left(4x-32\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 4x-32=0.

$$x=0 x=8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x-6 ki te 4.

$$\left(4x-24\right)x=x\times 8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-24 ki te x.

$$4x^{2}-24x=x\times 8$$

Tangohia te x\times 8 mai i ngā taha e rua.

$$4x^{2}-24x-x\times 8=0$$

Pahekotia te -24x me -x\times 8, ka -32x.

$$4x^{2}-32x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -32 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}}}{2\times 4}$$

Tuhia te pūtakerua o te \left(-32\right)^{2}.

$$x=\frac{-\left(-32\right)±32}{2\times 4}$$

Ko te tauaro o -32 ko 32.

$$x=\frac{32±32}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{32±32}{8}$$

Nā, me whakaoti te whārite x=\frac{32±32}{8} ina he tāpiri te ±. Tāpiri 32 ki te 32.

$$x=\frac{64}{8}$$

Whakawehe 64 ki te 8.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{32±32}{8} ina he tango te ±. Tango 32 mai i 32.

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

Whakawehe 0 ki te 8.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=8 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x-6 ki te 4.

$$\left(4x-24\right)x=x\times 8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-24 ki te x.

$$4x^{2}-24x=x\times 8$$

Tangohia te x\times 8 mai i ngā taha e rua.

$$4x^{2}-24x-x\times 8=0$$

Pahekotia te -24x me -x\times 8, ka -32x.

$$4x^{2}-32x=0$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}-32x}{4}=\frac{0}{4}$$

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

$$x^{2}+\left(-\frac{32}{4}\right)x=\frac{0}{4}$$

Whakawehe -32 ki te 4.

$$x^{2}-8x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

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

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 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 tāpiri 4 ki ngā taha e rua o te whārite.

$$x=8 x=0$$