Whakaoti i te 8x=4x^2

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

Whakaoti mō x

$$x=2$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

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

Tauwehea te x.

$$x\left(8-4x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 8-4x=0.

$$x=0 x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

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.

$$-4x^{2}+8x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4 mō a, 8 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 8^{2}.

$$x=\frac{-8±8}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-8±8}{-8}$$

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

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

Whakawehe 0 ki te -8.

$$x=0$$

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

$$x=-\frac{16}{-8}$$

Whakawehe -16 ki te -8.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=0 x=2$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

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.

$$-4x^{2}+8x=0$$

Whakawehea ngā taha e rua ki te -4.

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

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

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

Whakawehe 8 ki te -4.

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

Whakawehe 0 ki te -4.

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

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-2x+1=1$$

Tauwehea x^{2}-2x+1. 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}.

$$\left(x-1\right)^{2}=1$$

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

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

Whakarūnātia.

$$x-1=1 x-1=-1$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=2 x=0$$