Whakaoti i te 150/360pi(x^2)=60pi

$$\frac{ 150 }{ 360 } \pi ( { x }^{ 2 } )=60 \pi$$

Whakaoti mō x

$$x=12$$

$$x=-12$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Me whakakore te \pi ki ngā taha e rua.

$$\frac{150}{360}x^{2}=60$$

Whakahekea te hautanga \frac{150}{360} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 30.

$$\frac{5}{12}x^{2}=60$$

Tangohia te 60 mai i ngā taha e rua.

$$\frac{5}{12}x^{2}-60=0$$

Whakawehea ngā taha e rua ki te \frac{5}{12}.

$$x^{2}-144=0$$

Whakaarohia te x^{2}-144. Tuhia anō te x^{2}-144 hei x^{2}-12^{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).

$$\left(x-12\right)\left(x+12\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-12=0 me te x+12=0.

$$x=12 x=-12$$

Ngā Upane mā te Kimi Pūtakerua

Me whakakore te \pi ki ngā taha e rua.

$$\frac{150}{360}x^{2}=60$$

Whakahekea te hautanga \frac{150}{360} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 30.

$$\frac{5}{12}x^{2}=60$$

Me whakarea ngā taha e rua ki te \frac{12}{5}, te tau utu o \frac{5}{12}.

$$x^{2}=60\times \frac{12}{5}$$

Whakareatia te 60 ki te \frac{12}{5}, ka 144.

$$x^{2}=144$$

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

$$x=12 x=-12$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakakore te \pi ki ngā taha e rua.

$$\frac{150}{360}x^{2}=60$$

Whakahekea te hautanga \frac{150}{360} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 30.

$$\frac{5}{12}x^{2}=60$$

Tangohia te 60 mai i ngā taha e rua.

$$\frac{5}{12}x^{2}-60=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{5}{12} mō a, 0 mō b, me -60 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{5}{12}\left(-60\right)}}{2\times \frac{5}{12}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{5}{12}\left(-60\right)}}{2\times \frac{5}{12}}$$

Whakareatia -4 ki te \frac{5}{12}.

$$x=\frac{0±\sqrt{-\frac{5}{3}\left(-60\right)}}{2\times \frac{5}{12}}$$

Whakareatia -\frac{5}{3} ki te -60.

$$x=\frac{0±\sqrt{100}}{2\times \frac{5}{12}}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{0±10}{2\times \frac{5}{12}}$$

Whakareatia 2 ki te \frac{5}{12}.

$$x=\frac{0±10}{\frac{5}{6}}$$

Nā, me whakaoti te whārite x=\frac{0±10}{\frac{5}{6}} ina he tāpiri te ±. Whakawehe 10 ki te \frac{5}{6} mā te whakarea 10 ki te tau huripoki o \frac{5}{6}.

$$x=12$$

Nā, me whakaoti te whārite x=\frac{0±10}{\frac{5}{6}} ina he tango te ±. Whakawehe -10 ki te \frac{5}{6} mā te whakarea -10 ki te tau huripoki o \frac{5}{6}.

$$x=-12$$

Kua oti te whārite te whakatau.

$$x=12 x=-12$$