Whakaoti i te x=1/4x=

$$x= \frac{ 1 }{ 4x } =$$

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te \frac{1}{4x} mai i ngā taha e rua.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{4x}{4x}.

$$\frac{x\times 4x}{4x}-\frac{1}{4x}=0$$

Tā te mea he rite te tauraro o \frac{x\times 4x}{4x} me \frac{1}{4x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\times 4x-1}{4x}=0$$

Mahia ngā whakarea i roto o x\times 4x-1.

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

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 4x.

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

Whakaarohia te 4x^{2}-1. Tuhia anō te 4x^{2}-1 hei \left(2x\right)^{2}-1^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-1\right)\left(2x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te 2x-1=0 me te 2x+1=0.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te \frac{1}{4x} mai i ngā taha e rua.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{4x}{4x}.

$$\frac{x\times 4x}{4x}-\frac{1}{4x}=0$$

Tā te mea he rite te tauraro o \frac{x\times 4x}{4x} me \frac{1}{4x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\times 4x-1}{4x}=0$$

Mahia ngā whakarea i roto o x\times 4x-1.

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

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 4x.

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

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$4x^{2}=1$$

Whakawehea ngā taha e rua ki te 4.

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

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

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te \frac{1}{4x} mai i ngā taha e rua.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{4x}{4x}.

$$\frac{x\times 4x}{4x}-\frac{1}{4x}=0$$

Tā te mea he rite te tauraro o \frac{x\times 4x}{4x} me \frac{1}{4x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\times 4x-1}{4x}=0$$

Mahia ngā whakarea i roto o x\times 4x-1.

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

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 4x.

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

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

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-1\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-1\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-1\right)}}{2\times 4}$$

Whakareatia -16 ki te -1.

$$x=\frac{0±\sqrt{16}}{2\times 4}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{0±4}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±4}{8}$$

Nā, me whakaoti te whārite x=\frac{0±4}{8} ina he tāpiri te ±. Whakahekea te hautanga \frac{4}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{0±4}{8} ina he tango te ±. Whakahekea te hautanga \frac{-4}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=-\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{2} x=-\frac{1}{2}$$