Whakaoti i te 2x^2-3=15

$$2 x ^ { 2 } - 3 = 15$$

Whakaoti mō x

$$x=3$$

$$x=-3$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 15 mai i ngā taha e rua.

$$2x^{2}-3-15=0$$

Tangohia te 15 i te -3, ka -18.

$$2x^{2}-18=0$$

Whakawehea ngā taha e rua ki te 2.

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

Whakaarohia te x^{2}-9. Tuhia anō te x^{2}-9 hei x^{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).

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

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

$$x=3 x=-3$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 3 ki ngā taha e rua.

$$2x^{2}=15+3$$

Tāpirihia te 15 ki te 3, ka 18.

$$2x^{2}=18$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{18}{2}$$

Whakawehea te 18 ki te 2, kia riro ko 9.

$$x^{2}=9$$

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

$$x=3 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 15 mai i ngā taha e rua.

$$2x^{2}-3-15=0$$

Tangohia te 15 i te -3, ka -18.

$$2x^{2}-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-18\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\left(-18\right)}}{2\times 2}$$

Whakareatia -8 ki te -18.

$$x=\frac{0±\sqrt{144}}{2\times 2}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{0±12}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±12}{4}$$

Nā, me whakaoti te whārite x=\frac{0±12}{4} ina he tāpiri te ±. Whakawehe 12 ki te 4.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{0±12}{4} ina he tango te ±. Whakawehe -12 ki te 4.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=3 x=-3$$