Whakaoti i te 4x^2=-8x

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

Whakaoti mō x

$$x=-2$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 8x ki ngā taha e rua.

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

Tauwehea te x.

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

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

$$x=0 x=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 8x ki ngā taha e rua.

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

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}.

$$x=\frac{-8±\sqrt{8^{2}}}{2\times 4}$$

Tuhia te pūtakerua o te 8^{2}.

$$x=\frac{-8±8}{2\times 4}$$

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

Me tāpiri te 8x ki ngā taha e rua.

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

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.

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

Pūrua 1.

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

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 tango 1 mai i ngā taha e rua o te whārite.

$$x=0 x=-2$$