Whakaoti i te 120000=112*812{left(x/1000right)}^2

$$120000 = 112 \cdot 812 { \left( \frac{ x }{ 1000 } \right) }^{ 2 }$$

Whakaoti mō x

$$x = \frac{25000 \sqrt{87}}{203} \approx 1148.692001612$$

$$x = -\frac{25000 \sqrt{87}}{203} \approx -1148.692001612$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 112 ki te 812, ka 90944.

$$120000=90944\times \left(\frac{x}{1000}\right)^{2}$$

Kia whakarewa i te \frac{x}{1000} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$120000=90944\times \frac{x^{2}}{1000^{2}}$$

Tuhia te 90944\times \frac{x^{2}}{1000^{2}} hei hautanga kotahi.

$$120000=\frac{90944x^{2}}{1000^{2}}$$

Tātaihia te 1000 mā te pū o 2, kia riro ko 1000000.

$$120000=\frac{90944x^{2}}{1000000}$$

Whakawehea te 90944x^{2} ki te 1000000, kia riro ko \frac{1421}{15625}x^{2}.

$$120000=\frac{1421}{15625}x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{1421}{15625}x^{2}=120000$$

Me whakarea ngā taha e rua ki te \frac{15625}{1421}, te tau utu o \frac{1421}{15625}.

$$x^{2}=120000\times \frac{15625}{1421}$$

Whakareatia te 120000 ki te \frac{15625}{1421}, ka \frac{1875000000}{1421}.

$$x^{2}=\frac{1875000000}{1421}$$

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

$$x=\frac{25000\sqrt{87}}{203} x=-\frac{25000\sqrt{87}}{203}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 112 ki te 812, ka 90944.

$$120000=90944\times \left(\frac{x}{1000}\right)^{2}$$

Kia whakarewa i te \frac{x}{1000} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$120000=90944\times \frac{x^{2}}{1000^{2}}$$

Tuhia te 90944\times \frac{x^{2}}{1000^{2}} hei hautanga kotahi.

$$120000=\frac{90944x^{2}}{1000^{2}}$$

Tātaihia te 1000 mā te pū o 2, kia riro ko 1000000.

$$120000=\frac{90944x^{2}}{1000000}$$

Whakawehea te 90944x^{2} ki te 1000000, kia riro ko \frac{1421}{15625}x^{2}.

$$120000=\frac{1421}{15625}x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{1421}{15625}x^{2}=120000$$

Tangohia te 120000 mai i ngā taha e rua.

$$\frac{1421}{15625}x^{2}-120000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1421}{15625} mō a, 0 mō b, me -120000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1421}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{1421}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

Whakareatia -4 ki te \frac{1421}{15625}.

$$x=\frac{0±\sqrt{-\frac{5684}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

Whakareatia -\frac{5684}{15625} ki te -120000.

$$x=\frac{0±\sqrt{\frac{1091328}{25}}}{2\times \frac{1421}{15625}}$$

Tuhia te pūtakerua o te \frac{1091328}{25}.

$$x=\frac{0±\frac{112\sqrt{87}}{5}}{2\times \frac{1421}{15625}}$$

Whakareatia 2 ki te \frac{1421}{15625}.

$$x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}} ina he tāpiri te ±.

$$x=\frac{25000\sqrt{87}}{203}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}} ina he tango te ±.

$$x=-\frac{25000\sqrt{87}}{203}$$

Kua oti te whārite te whakatau.

$$x=\frac{25000\sqrt{87}}{203} x=-\frac{25000\sqrt{87}}{203}$$