Whakaoti i te 4x^2-30=34

$$4 x ^ { 2 } - 30 = 34$$

Whakaoti mō x

$$x=4$$

$$x=-4$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 34 mai i ngā taha e rua.

$$4x^{2}-30-34=0$$

Tangohia te 34 i te -30, ka -64.

$$4x^{2}-64=0$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}-16=0$$

Whakaarohia te x^{2}-16. Tuhia anō te x^{2}-16 hei x^{2}-4^{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).

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

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

$$x=4 x=-4$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 30 ki ngā taha e rua.

$$4x^{2}=34+30$$

Tāpirihia te 34 ki te 30, ka 64.

$$4x^{2}=64$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{64}{4}$$

Whakawehea te 64 ki te 4, kia riro ko 16.

$$x^{2}=16$$

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

$$x=4 x=-4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 34 mai i ngā taha e rua.

$$4x^{2}-30-34=0$$

Tangohia te 34 i te -30, ka -64.

$$4x^{2}-64=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -64 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-64\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-64\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-64\right)}}{2\times 4}$$

Whakareatia -16 ki te -64.

$$x=\frac{0±\sqrt{1024}}{2\times 4}$$

Tuhia te pūtakerua o te 1024.

$$x=\frac{0±32}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±32}{8}$$

Nā, me whakaoti te whārite x=\frac{0±32}{8} ina he tāpiri te ±. Whakawehe 32 ki te 8.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{0±32}{8} ina he tango te ±. Whakawehe -32 ki te 8.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=4 x=-4$$