Whakaoti i te (4x)^2=576

$$( 4 x ) ^ { 2 } = 576$$

Whakaoti mō x

$$x=6$$

$$x=-6$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakarohaina te \left(4x\right)^{2}.

$$4^{2}x^{2}=576$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16x^{2}=576$$

Tangohia te 576 mai i ngā taha e rua.

$$16x^{2}-576=0$$

Whakawehea ngā taha e rua ki te 16.

$$x^{2}-36=0$$

Whakaarohia te x^{2}-36. Tuhia anō te x^{2}-36 hei x^{2}-6^{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).

$$\left(x-6\right)\left(x+6\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-6=0 me te x+6=0.

$$x=6 x=-6$$

Ngā Upane mā te Kimi Pūtakerua

Whakarohaina te \left(4x\right)^{2}.

$$4^{2}x^{2}=576$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16x^{2}=576$$

Whakawehea ngā taha e rua ki te 16.

$$x^{2}=\frac{576}{16}$$

Whakawehea te 576 ki te 16, kia riro ko 36.

$$x^{2}=36$$

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

$$x=6 x=-6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(4x\right)^{2}.

$$4^{2}x^{2}=576$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16x^{2}=576$$

Tangohia te 576 mai i ngā taha e rua.

$$16x^{2}-576=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 16 mō a, 0 mō b, me -576 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-576\right)}}{2\times 16}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-576\right)}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$x=\frac{0±\sqrt{-64\left(-576\right)}}{2\times 16}$$

Whakareatia -64 ki te -576.

$$x=\frac{0±\sqrt{36864}}{2\times 16}$$

Tuhia te pūtakerua o te 36864.

$$x=\frac{0±192}{2\times 16}$$

Whakareatia 2 ki te 16.

$$x=\frac{0±192}{32}$$

Nā, me whakaoti te whārite x=\frac{0±192}{32} ina he tāpiri te ±. Whakawehe 192 ki te 32.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{0±192}{32} ina he tango te ±. Whakawehe -192 ki te 32.

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=6 x=-6$$