Whakaoti i te 2=4(x^2-7/4)

$$2=4( { x }^{ 2 } - \frac{ 7 }{ 4 } )$$

Whakaoti mō x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 4.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

Tangohia te \frac{1}{2} mai i ngā taha e rua.

$$x^{2}-\frac{7}{4}-\frac{1}{2}=0$$

Tangohia te \frac{1}{2} i te -\frac{7}{4}, ka -\frac{9}{4}.

$$x^{2}-\frac{9}{4}=0$$

Me whakarea ngā taha e rua ki te 4.

$$4x^{2}-9=0$$

Whakaarohia te 4x^{2}-9. Tuhia anō te 4x^{2}-9 hei \left(2x\right)^{2}-3^{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).

$$\left(2x-3\right)\left(2x+3\right)=0$$

Hei kimi otinga whārite, me whakaoti te 2x-3=0 me te 2x+3=0.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Ngā Upane mā te Kimi Pūtakerua

Whakawehea ngā taha e rua ki te 4.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

Me tāpiri te \frac{7}{4} ki ngā taha e rua.

$$x^{2}=\frac{1}{2}+\frac{7}{4}$$

Tāpirihia te \frac{1}{2} ki te \frac{7}{4}, ka \frac{9}{4}.

$$x^{2}=\frac{9}{4}$$

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

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 4.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

Tangohia te \frac{1}{2} mai i ngā taha e rua.

$$x^{2}-\frac{7}{4}-\frac{1}{2}=0$$

Tangohia te \frac{1}{2} i te -\frac{7}{4}, ka -\frac{9}{4}.

$$x^{2}-\frac{9}{4}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{9}{4} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{4}\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{9}{4}\right)}}{2}$$

Whakareatia -4 ki te -\frac{9}{4}.

$$x=\frac{0±\sqrt{9}}{2}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{0±3}{2}$$

Nā, me whakaoti te whārite x=\frac{0±3}{2} ina he tāpiri te ±. Whakawehe 3 ki te 2.

$$x=\frac{3}{2}$$

Nā, me whakaoti te whārite x=\frac{0±3}{2} ina he tango te ±. Whakawehe -3 ki te 2.

$$x=-\frac{3}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{2} x=-\frac{3}{2}$$