Whakaoti i te 180/360(x^2)*pi=50pi

$$\frac{ 180 }{ 360 } ( { x }^{ 2 } ) \times \pi =50 \pi$$

Whakaoti mō x

$$x=10$$

$$x=-10$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Me whakakore te \pi ki ngā taha e rua.

$$\frac{180}{360}x^{2}=50$$

Whakahekea te hautanga \frac{180}{360} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 180.

$$\frac{1}{2}x^{2}=50$$

Tangohia te 50 mai i ngā taha e rua.

$$\frac{1}{2}x^{2}-50=0$$

Me whakarea ngā taha e rua ki te 2.

$$x^{2}-100=0$$

Whakaarohia te x^{2}-100. Tuhia anō te x^{2}-100 hei x^{2}-10^{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).

$$\left(x-10\right)\left(x+10\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-10=0 me te x+10=0.

$$x=10 x=-10$$

Ngā Upane mā te Kimi Pūtakerua

Me whakakore te \pi ki ngā taha e rua.

$$\frac{180}{360}x^{2}=50$$

Whakahekea te hautanga \frac{180}{360} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 180.

$$\frac{1}{2}x^{2}=50$$

Me whakarea ngā taha e rua ki te 2, te tau utu o \frac{1}{2}.

$$x^{2}=50\times 2$$

Whakareatia te 50 ki te 2, ka 100.

$$x^{2}=100$$

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

$$x=10 x=-10$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakakore te \pi ki ngā taha e rua.

$$\frac{180}{360}x^{2}=50$$

Whakahekea te hautanga \frac{180}{360} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 180.

$$\frac{1}{2}x^{2}=50$$

Tangohia te 50 mai i ngā taha e rua.

$$\frac{1}{2}x^{2}-50=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{2} mō a, 0 mō b, me -50 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-50\right)}}{2\times \frac{1}{2}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-50\right)}}{2\times \frac{1}{2}}$$

Whakareatia -4 ki te \frac{1}{2}.

$$x=\frac{0±\sqrt{-2\left(-50\right)}}{2\times \frac{1}{2}}$$

Whakareatia -2 ki te -50.

$$x=\frac{0±\sqrt{100}}{2\times \frac{1}{2}}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{0±10}{2\times \frac{1}{2}}$$

Whakareatia 2 ki te \frac{1}{2}.

$$x=\frac{0±10}{1}$$

Nā, me whakaoti te whārite x=\frac{0±10}{1} ina he tāpiri te ±.

$$x=10$$

Nā, me whakaoti te whārite x=\frac{0±10}{1} ina he tango te ±.

$$x=-10$$

Kua oti te whārite te whakatau.

$$x=10 x=-10$$